Contents of this Precalculus episode:

Special types of matrices, Square matrix, Diagonal matrix, Identity matrix, Transpose, Symmetric matrix.

SQUARE MATRIX

It is a square-shaped matrix with the same number of rows and columns.

Example:

DIAGONAL MATRIX

The diagonal matrix is a square matrix where all elements outside the main diagonal are zero.

Example:

Therefore, in diagonal matrices, only the main diagonal matters, as all the other elements are zero.

That's why some people only indicate the main diagonal elements. This strange symbol

indicates a diagonal matrix.

IDENTITY MATRIX

The identity matrix (or unit matrix), denoted by I, is a matrix where for any , .

The identity matrix is a diagonal matrix where all elements on the main diagonal are equal to one.

INVERSE MATRIX

The inverse matrix is denoted by , and this is a matrix that does this:

(right inverse) (left inverse)

Later we will see that it isn't that easy to figure out the inverse of a matrix.

This inverse thing is a lot easier with real numbers where:

the inverse of is because

the inverse of is because

TRANSPOSE

The transpose matrix is created by swapping the rows and the columns of the matrix. It is indicated by or

ROW COLUMN COLUMN ROW

Example:

OR

A square matrix whose transpose is equal to itself is called a symmetric matrix.

Here is an example of a symmetric matrix:

None of this sounds too exciting right now, but soon will come the time when we will need them.

Now, let's take on vectors!

Precalculus episode