Matrix Properties / Features

Now that we know what a matrix is, let's see what features matrices have, and get to know some special matrices.

Learning matrix features is important since when we learn about matrix operations in several slides from know, we'll need to verify whether a matrix has a certain feature before using it in an operation.

1. Matrix size. Each matrix is built from rows and columns of elements:
   • Rows are horizontal arrays of elements, and
   • Columns are vertical arrays of elements running throughout the matrix.
   Let $n$ be equal to the number of rows and $m$ equal to the number of columns in some matrix $A$.
   • The size (also called: dimensions or order) of $A$ is denoted as $n \times m$ (

     $n \times m$

     ).
   • The matrix $A_{n \times m}$ (

     $A_{n \times m}$

     ) or $A_{n, m}$ (

     $A_{n, m}$

     ) is a matrix with $n$ rows and $m$ columns.
     • $A$ is then called an $n \times m$ matrix (read as "An $n$ by $m$ matrix").
   • Knowing what the size of a matrix is will help us decide whether a certain matrix operation is applicable or not.