Matrix Definitions

I will add to this page as I progress through matrices…

First off a matrix is a "rectangular array" of numbers. Or in other words a bunch of numbers that are arranged in rows and columns. For example:

(1)
\begin{pmatrix} 1 & 3 & 3\\ 4 & 5 & 6\\ 7 & 9& 2 \end{pmatrix}

The above matrix is of the order 3 x 3. Where the order is defined as the number of rows (3) by the number of columns (3). The following matrix is of order 3 x 2.

(2)
\begin{pmatrix} 1 & 3 \\ 4 & 5 \\ 7 & 9 \end{pmatrix}

A row is defined as, well, a row… In the case above the numbers 1 and 3 are the first row and 7 and 9 are the third row. A column is likewise defined to be a column of numbers. In the case above 1 4 and 7 form the first column and 3 5 and 9 form the second column.

We often talk about an element of a matrix. In this case we are referring to a specific value. For example I might refer to the element in the second row and first column, which would be 4 in both examples above.

Notation

Matrices are often give an UPPER CASE letter as a symbol. For example:

(3)
\begin{align} A= \begin{pmatrix} 1 & 3 & 3\\ 4 & 5 & 6\\ 7 & 9& 2 \end{pmatrix} \end{align}

An element in the matrix A can be denoted by $a_{i,j}$, where the lower case a implies a connection to matrix A and the subscripts correlate to the row and column, respectively. For example $a_{3,3}=2$.

When scalar (regular) variables and matrix variables are shown together the matrix symbol(s) are often in bold for added clarity.
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