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26

2

$begingroup$

A simple question: By definition, does an m x n matrix have m rows and n columns, or is it vice versa?

matrices

share|cite|improve this question

asked Sep 6 '12 at 2:15

Anderson GreenAnderson Green

40571322

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes it's always "{number of rows} by {number of columns}"
  $endgroup$
  – Colonel Panic
  Feb 18 '15 at 16:15
  
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  You can name the variables how you like though. Curiously "m by n matrix" is about twice as common as "n by m matrix" in Google search results.
  $endgroup$
  – Colonel Panic
  Feb 18 '15 at 16:19
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @ColonelPanic, that's probably because for a matrix $A$ operating on an $n$ dimensional vector $mathcal{x}$ (i.e. $A mathbf{x} = mathbf{y}$) $mathbf{y}$ is $m$ dimensional. In other words, it puts the input dimension before the output dimension alphabetically.
  $endgroup$
  – Shep
  Apr 3 '15 at 1:42
  
  
  

  
  
  
  

add a comment | 

26

2

$begingroup$

A simple question: By definition, does an m x n matrix have m rows and n columns, or is it vice versa?

matrices

share|cite|improve this question

asked Sep 6 '12 at 2:15

Anderson GreenAnderson Green

40571322

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes it's always "{number of rows} by {number of columns}"
  $endgroup$
  – Colonel Panic
  Feb 18 '15 at 16:15
  
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  You can name the variables how you like though. Curiously "m by n matrix" is about twice as common as "n by m matrix" in Google search results.
  $endgroup$
  – Colonel Panic
  Feb 18 '15 at 16:19
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @ColonelPanic, that's probably because for a matrix $A$ operating on an $n$ dimensional vector $mathcal{x}$ (i.e. $A mathbf{x} = mathbf{y}$) $mathbf{y}$ is $m$ dimensional. In other words, it puts the input dimension before the output dimension alphabetically.
  $endgroup$
  – Shep
  Apr 3 '15 at 1:42
  
  
  

  
  
  
  

add a comment | 

$begingroup$

A simple question: By definition, does an m x n matrix have m rows and n columns, or is it vice versa?

matrices

share|cite|improve this question

asked Sep 6 '12 at 2:15

Anderson GreenAnderson Green

40571322

$endgroup$

share|cite|improve this question

asked Sep 6 '12 at 2:15

Anderson GreenAnderson Green

40571322

share|cite|improve this question

asked Sep 6 '12 at 2:15

Anderson GreenAnderson Green

40571322

asked Sep 6 '12 at 2:15

Anderson GreenAnderson Green

40571322

asked Sep 6 '12 at 2:15

Anderson GreenAnderson Green

40571322

4 Answers
4

active

oldest

votes

22

$begingroup$

An $m times n$ matrix has $m$ rows and $n$ columns.

share|cite|improve this answer

edited Aug 13 '15 at 21:52

Zhanxiong

8,94911032

answered Sep 6 '12 at 2:16

JamesJames

62511421

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  can you provide a reference/citation for this?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:16
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  All the textbooks i have read (both cs and math) have used this notation. For example, Strang's Introduction to Linear Algebra 4th.
  $endgroup$
  – James
  Sep 6 '12 at 2:17
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You said "almost all". Were there any exceptions?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:19
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, I meant all.
  $endgroup$
  – James
  Sep 6 '12 at 2:20
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @IvanBalashov In Numpy the first dimension is the row, not the column.
  $endgroup$
  – bfontaine
  Oct 22 '16 at 7:36
  

  
  
  
  

 | 
show 3 more comments

1

$begingroup$

I suggest you always to check the notation on the book which you are using. I found sometimes this notation with different meaning. In advanced books, for example. Even the notation for linear maps as matrices. Sometimes they write $xT$.

share|cite|improve this answer

answered Sep 6 '12 at 2:28

SigurSigur

4,50311736

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What does xT refer to in this case?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is the notation for the image of $x$ by the linear map $T$. Usually we write $T(x)$ or $Tx$.
  $endgroup$
  – Sigur
  Sep 6 '12 at 2:38
  

  
  
  
  

add a comment | 

1

$begingroup$

Always check and make sure you have the right convention for the occasion. Usually m x n is rows x columns. I like to remember this as being in REVERSE alphabetical order - Rows by Columns, or R first then C. However, in Boyce & DiPrima's book "Elementary Differential Equations and Boundary Value Problems" an m x n matrix has m vertical columns and n horizontal rows.

However, when addressing elements within a matrix, it's the opposite. The element "a sub i,j" references the element in the ith row and jth column.
Lesson? Always check to make sure you have the correct convention!

share|cite|improve this answer

answered Jun 4 '15 at 21:56

SeanSean

211

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  so much for the "universal language of mathematics" :(
  $endgroup$
  – Robert Lugg
  Jan 21 at 17:32
  

  
  
  
  

add a comment | 

1

$begingroup$

Yes... It's m-rows and n-Columns.

Here is an example, how you can generate and read a matrix in JavaScript :)

let createMatrix = (m, n) => {

  let [row, column] = [[], []],

      rowColumn = m * n

  for (let i = 1; i <= rowColumn; i++) {

    column.push(i)

    if (i % n === 0) {

      row.push(column)

      column = []

    }

  }

  return row

}



let setColorForEachElement = (matrix, colors) => {

  let row = matrix.map(row => {

    let column = row.map((column, key) => {

      return { number: column, color: colors[key] }

    })

    return column

  })

  return row

} 



const colors = ['red', 'green', 'blue', 'purple', 'brown', 'yellow', 'orange', 'grey']

const matrix = createMatrix(6, 8)

const colorApi = setColorForEachElement(matrix, colors)



let table ='<table>'

colorApi.forEach(row => {

  table+='<tr>'

    row.forEach(column =>  table +=`<td style='background: ${column.color};'>${column.number}<td>` )

  table+='</tr>'

})



document.write(table);

share|cite|improve this answer

edited Mar 13 at 23:21

answered Mar 13 at 23:08

Driton HaxhiuDriton Haxhiu

113

$endgroup$

add a comment | 

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22

$begingroup$

An $m times n$ matrix has $m$ rows and $n$ columns.

share|cite|improve this answer

edited Aug 13 '15 at 21:52

Zhanxiong

8,94911032

answered Sep 6 '12 at 2:16

JamesJames

62511421

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  can you provide a reference/citation for this?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:16
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  All the textbooks i have read (both cs and math) have used this notation. For example, Strang's Introduction to Linear Algebra 4th.
  $endgroup$
  – James
  Sep 6 '12 at 2:17
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You said "almost all". Were there any exceptions?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:19
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, I meant all.
  $endgroup$
  – James
  Sep 6 '12 at 2:20
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @IvanBalashov In Numpy the first dimension is the row, not the column.
  $endgroup$
  – bfontaine
  Oct 22 '16 at 7:36
  

  
  
  
  

 | 
show 3 more comments

22

$begingroup$

An $m times n$ matrix has $m$ rows and $n$ columns.

share|cite|improve this answer

edited Aug 13 '15 at 21:52

Zhanxiong

8,94911032

answered Sep 6 '12 at 2:16

JamesJames

62511421

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  can you provide a reference/citation for this?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:16
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  All the textbooks i have read (both cs and math) have used this notation. For example, Strang's Introduction to Linear Algebra 4th.
  $endgroup$
  – James
  Sep 6 '12 at 2:17
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You said "almost all". Were there any exceptions?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:19
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, I meant all.
  $endgroup$
  – James
  Sep 6 '12 at 2:20
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @IvanBalashov In Numpy the first dimension is the row, not the column.
  $endgroup$
  – bfontaine
  Oct 22 '16 at 7:36
  

  
  
  
  

 | 
show 3 more comments

$begingroup$

An $m times n$ matrix has $m$ rows and $n$ columns.

share|cite|improve this answer

edited Aug 13 '15 at 21:52

Zhanxiong

8,94911032

answered Sep 6 '12 at 2:16

JamesJames

62511421

$endgroup$

share|cite|improve this answer

edited Aug 13 '15 at 21:52

Zhanxiong

8,94911032

answered Sep 6 '12 at 2:16

JamesJames

62511421

edited Aug 13 '15 at 21:52

Zhanxiong

8,94911032

edited Aug 13 '15 at 21:52

Zhanxiong

8,94911032

answered Sep 6 '12 at 2:16

JamesJames

62511421

answered Sep 6 '12 at 2:16

JamesJames

62511421

1

$begingroup$

I suggest you always to check the notation on the book which you are using. I found sometimes this notation with different meaning. In advanced books, for example. Even the notation for linear maps as matrices. Sometimes they write $xT$.

share|cite|improve this answer

answered Sep 6 '12 at 2:28

SigurSigur

4,50311736

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What does xT refer to in this case?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is the notation for the image of $x$ by the linear map $T$. Usually we write $T(x)$ or $Tx$.
  $endgroup$
  – Sigur
  Sep 6 '12 at 2:38
  

  
  
  
  

add a comment | 

1

$begingroup$

I suggest you always to check the notation on the book which you are using. I found sometimes this notation with different meaning. In advanced books, for example. Even the notation for linear maps as matrices. Sometimes they write $xT$.

share|cite|improve this answer

answered Sep 6 '12 at 2:28

SigurSigur

4,50311736

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What does xT refer to in this case?
  $endgroup$
  – Anderson Green
  Sep 6 '12 at 2:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is the notation for the image of $x$ by the linear map $T$. Usually we write $T(x)$ or $Tx$.
  $endgroup$
  – Sigur
  Sep 6 '12 at 2:38
  

  
  
  
  

add a comment | 

$begingroup$

I suggest you always to check the notation on the book which you are using. I found sometimes this notation with different meaning. In advanced books, for example. Even the notation for linear maps as matrices. Sometimes they write $xT$.

share|cite|improve this answer

answered Sep 6 '12 at 2:28

SigurSigur

4,50311736

$endgroup$

share|cite|improve this answer

answered Sep 6 '12 at 2:28

SigurSigur

4,50311736

answered Sep 6 '12 at 2:28

SigurSigur

4,50311736

answered Sep 6 '12 at 2:28

SigurSigur

4,50311736

1

$begingroup$

Always check and make sure you have the right convention for the occasion. Usually m x n is rows x columns. I like to remember this as being in REVERSE alphabetical order - Rows by Columns, or R first then C. However, in Boyce & DiPrima's book "Elementary Differential Equations and Boundary Value Problems" an m x n matrix has m vertical columns and n horizontal rows.

However, when addressing elements within a matrix, it's the opposite. The element "a sub i,j" references the element in the ith row and jth column.
Lesson? Always check to make sure you have the correct convention!

share|cite|improve this answer

answered Jun 4 '15 at 21:56

SeanSean

211

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  so much for the "universal language of mathematics" :(
  $endgroup$
  – Robert Lugg
  Jan 21 at 17:32
  

  
  
  
  

add a comment | 

1

$begingroup$

Always check and make sure you have the right convention for the occasion. Usually m x n is rows x columns. I like to remember this as being in REVERSE alphabetical order - Rows by Columns, or R first then C. However, in Boyce & DiPrima's book "Elementary Differential Equations and Boundary Value Problems" an m x n matrix has m vertical columns and n horizontal rows.

However, when addressing elements within a matrix, it's the opposite. The element "a sub i,j" references the element in the ith row and jth column.
Lesson? Always check to make sure you have the correct convention!

share|cite|improve this answer

answered Jun 4 '15 at 21:56

SeanSean

211

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  so much for the "universal language of mathematics" :(
  $endgroup$
  – Robert Lugg
  Jan 21 at 17:32
  

  
  
  
  

add a comment | 

$begingroup$

Always check and make sure you have the right convention for the occasion. Usually m x n is rows x columns. I like to remember this as being in REVERSE alphabetical order - Rows by Columns, or R first then C. However, in Boyce & DiPrima's book "Elementary Differential Equations and Boundary Value Problems" an m x n matrix has m vertical columns and n horizontal rows.

However, when addressing elements within a matrix, it's the opposite. The element "a sub i,j" references the element in the ith row and jth column.
Lesson? Always check to make sure you have the correct convention!

share|cite|improve this answer

answered Jun 4 '15 at 21:56

SeanSean

211

$endgroup$

share|cite|improve this answer

answered Jun 4 '15 at 21:56

SeanSean

211

answered Jun 4 '15 at 21:56

SeanSean

211

answered Jun 4 '15 at 21:56

SeanSean

211

1

$begingroup$

Yes... It's m-rows and n-Columns.

Here is an example, how you can generate and read a matrix in JavaScript :)

let createMatrix = (m, n) => {

  let [row, column] = [[], []],

      rowColumn = m * n

  for (let i = 1; i <= rowColumn; i++) {

    column.push(i)

    if (i % n === 0) {

      row.push(column)

      column = []

    }

  }

  return row

}



let setColorForEachElement = (matrix, colors) => {

  let row = matrix.map(row => {

    let column = row.map((column, key) => {

      return { number: column, color: colors[key] }

    })

    return column

  })

  return row

} 



const colors = ['red', 'green', 'blue', 'purple', 'brown', 'yellow', 'orange', 'grey']

const matrix = createMatrix(6, 8)

const colorApi = setColorForEachElement(matrix, colors)



let table ='<table>'

colorApi.forEach(row => {

  table+='<tr>'

    row.forEach(column =>  table +=`<td style='background: ${column.color};'>${column.number}<td>` )

  table+='</tr>'

})



document.write(table);

share|cite|improve this answer

edited Mar 13 at 23:21

answered Mar 13 at 23:08

Driton HaxhiuDriton Haxhiu

113

$endgroup$

add a comment | 

1

$begingroup$

Yes... It's m-rows and n-Columns.

Here is an example, how you can generate and read a matrix in JavaScript :)

let createMatrix = (m, n) => {

  let [row, column] = [[], []],

      rowColumn = m * n

  for (let i = 1; i <= rowColumn; i++) {

    column.push(i)

    if (i % n === 0) {

      row.push(column)

      column = []

    }

  }

  return row

}



let setColorForEachElement = (matrix, colors) => {

  let row = matrix.map(row => {

    let column = row.map((column, key) => {

      return { number: column, color: colors[key] }

    })

    return column

  })

  return row

} 



const colors = ['red', 'green', 'blue', 'purple', 'brown', 'yellow', 'orange', 'grey']

const matrix = createMatrix(6, 8)

const colorApi = setColorForEachElement(matrix, colors)



let table ='<table>'

colorApi.forEach(row => {

  table+='<tr>'

    row.forEach(column =>  table +=`<td style='background: ${column.color};'>${column.number}<td>` )

  table+='</tr>'

})



document.write(table);

share|cite|improve this answer

edited Mar 13 at 23:21

answered Mar 13 at 23:08

Driton HaxhiuDriton Haxhiu

113

$endgroup$

add a comment | 

$begingroup$

Yes... It's m-rows and n-Columns.

Here is an example, how you can generate and read a matrix in JavaScript :)

let createMatrix = (m, n) => {

  let [row, column] = [[], []],

      rowColumn = m * n

  for (let i = 1; i <= rowColumn; i++) {

    column.push(i)

    if (i % n === 0) {

      row.push(column)

      column = []

    }

  }

  return row

}



let setColorForEachElement = (matrix, colors) => {

  let row = matrix.map(row => {

    let column = row.map((column, key) => {

      return { number: column, color: colors[key] }

    })

    return column

  })

  return row

} 



const colors = ['red', 'green', 'blue', 'purple', 'brown', 'yellow', 'orange', 'grey']

const matrix = createMatrix(6, 8)

const colorApi = setColorForEachElement(matrix, colors)



let table ='<table>'

colorApi.forEach(row => {

  table+='<tr>'

    row.forEach(column =>  table +=`<td style='background: ${column.color};'>${column.number}<td>` )

  table+='</tr>'

})



document.write(table);

share|cite|improve this answer

edited Mar 13 at 23:21

answered Mar 13 at 23:08

Driton HaxhiuDriton Haxhiu

113

$endgroup$

let createMatrix = (m, n) => {

  let [row, column] = [[], []],

      rowColumn = m * n

  for (let i = 1; i <= rowColumn; i++) {

    column.push(i)

    if (i % n === 0) {

      row.push(column)

      column = []

    }

  }

  return row

}



let setColorForEachElement = (matrix, colors) => {

  let row = matrix.map(row => {

    let column = row.map((column, key) => {

      return { number: column, color: colors[key] }

    })

    return column

  })

  return row

} 



const colors = ['red', 'green', 'blue', 'purple', 'brown', 'yellow', 'orange', 'grey']

const matrix = createMatrix(6, 8)

const colorApi = setColorForEachElement(matrix, colors)



let table ='<table>'

colorApi.forEach(row => {

  table+='<tr>'

    row.forEach(column =>  table +=`<td style='background: ${column.color};'>${column.number}<td>` )

  table+='</tr>'

})



document.write(table);

share|cite|improve this answer

edited Mar 13 at 23:21

answered Mar 13 at 23:08

Driton HaxhiuDriton Haxhiu

113

answered Mar 13 at 23:08

Driton HaxhiuDriton Haxhiu

113

answered Mar 13 at 23:08

Driton HaxhiuDriton Haxhiu

113