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12: Matrices

Last updated

Oct 19, 2022
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- 11.2.1: Review Problems
- 12.1: Linear Transformations and 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.

12.1: Linear Transformations and Matrices
Ordered, finite-dimensional, bases for vector spaces allows us to express linear operators as matrices.
- 12.1.1: Review Problems
12.2: 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.
- 12.2.1: Review Problems
12.3: 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 .
- 12.3.1: Review Problems
12.4: 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.
- 12.4.1: Review Problems

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

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

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