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?

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You're correct. An m x n matrix has m rows and n columns.

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can you provide a reference/citation for this? –  Anderson Green Sep 6 '12 at 2:16
All the textbooks i have read (both cs and math) have used this notation. For example, Strang's Introduction to Linear Algebra 4th. –  James Sep 6 '12 at 2:17
You said "almost all". Were there any exceptions? –  Anderson Green Sep 6 '12 at 2:19
Sorry, I meant all. –  James Sep 6 '12 at 2:20

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 $xT$.

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What does xT refer to in this case? –  Anderson Green Sep 6 '12 at 2:36
It is the notation for the image of $x$ by the linear map $T$. Usually we write $T(x)$ or $Tx$. –  Sigur Sep 6 '12 at 2:38