Matrices

A Matrix is an array of numbers:

A Matrix
(This one has 2 Rows and 3 Columns)

There are many things we can do with them ...

Adding

To add two matrices: add the numbers in the matching positions:

The two matrices must be the same size, i.e. the rows must match in size, and the columns must match in size.

Negative

The negative of a matrix is also simple:

Subtracting

To subtract two matrices: subtract the numbers in the matching positions:

Note: subtracting is actually defined as the addition of a negative matrix: A + (-B)

Multiply by a Constant

We can multiply a matrix by some value:

We call the constant a scalar, so officially this is called "scalar multiplication".

Multiplying by Another Matrix

To multiply two matrices together is a bit more difficult ... read Multiplying Matrices to learn how.

Dividing

And what about division? Well we don't actually divide matrices, we do it this way:

So we don't divide, instead we multiply by an inverse.

And there are special ways to find the Inverse ...

... learn more about the Inverse of a Matrix.

Transposing

To "transpose" a matrix, swap the rows and columns. We put a "T" in the top right-hand corner to mean transpose:

Notation

A matrix is usually shown by a capital letter (such as A, or B)

Each entry (or "element") is shown by a lower case letter with a "subscript" of row,column:

Rows and Columns So which is the row and which is the column? Rows go left-right Columns go up-down To remember that rows come before columns use the word "arc": ar,c