How many rows and columns are in an m x n matrix?
A simple question: By definition, does an m x n matrix have m rows and n columns, or is it vice versa?
4 Answers
$\begingroup$An $m \times n$ matrix has $m$ rows and $n$ columns.
$\endgroup$ 9 $\begingroup$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 $xT$.
$\endgroup$ 2 $\begingroup$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!
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);
