# 7: Matrices

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Matrices are a powerful tool for calculations involving linear transformations. It is important to understand how to find the matrix of a linear transformation and properties of matrices.

- 7.1: Linear Transformations and Matrices
- Ordered, finite-dimensional, bases for vector spaces allows us to express linear operators as matrices.

- 7.3: Properties of Matrices
- The objects of study in linear algebra are linear operators. We have seen that linear operators can be represented as matrices through choices of ordered bases, and that matrices provide a means of efficient computation.

- 7.5: Inverse Matrix
- A square matrix MM is invertible (or nonsingular) if there exists a matrix M⁻¹ such that M⁻¹M=I=M⁻¹M. If M has no inverse, we say M is Singular or non-invertible .

- 7.7: LU Redux
- Certain matrices are easier to work with than others. In this section, we will see how to write any square matrix M as the product of two simpler matrices.

*Thumbnail: Overview of a matrix (CC BY-SA 3.0; Lakeworks)*

### Contributor

David Cherney, Tom Denton, and Andrew Waldron (UC Davis)