## Eigenvalues and Eigenvectors

Eigenvectors are a special type of vector related to linear transformations. It is a vector with the property that when…

## Matrix Inverses and Cramer’s Rule

Determinates can be used to find inverses of matrices, as well as solutions to linear systems in general. We may…

## Elementary Row Operators and Determinates

From the previous section, we saw that the process of calculating a determinate can be long and complex. Due to…

## Determinates in Terms of Cofactors

For square matrices, we can calculate a special value called the determinate. This value has a few uses, most notably,…

## Identity and Inverse Matrices

Suppose that we have a matrix A, and we wish to find a matrix I, with the property that AI…

## Geometric Transformations

Geometric transformations are an example of a mapping used to manipulate vectors in space. They are typically used to do…

## Matrix and Linear Mapings

With matrix multiplication, we can extend the ways that we manipulate matrices. One method of doing this is matrix mappings…

## Matrix Multiplication

We discussed that scalar multiplication applies to matrices by multiplying the scalar by each component in the matrix. In order…

## Matrix Transposes

The transpose operation is one that allows us to swap the rows and columns of a matrix. For example, suppose…

## Matrix Operations

Now that we have introduced how matrices are used in linear systems, we can look at the operations and properties…