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Category: Linear Algebra

Eigenvalues and Eigenvectors

November 21, 2019 Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Matrix Inverses and Cramer’s Rule

November 19, 2019 Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Elementary Row Operators and Determinates

Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Determinates in Terms of Cofactors

November 13, 2019 Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Identity and Inverse Matrices

Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Geometric Transformations

November 11, 2019 Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Matrix and Linear Mapings

Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Matrix Multiplication

November 9, 2019 Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Matrix Transposes

Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

Matrix Operations

Scott Cosentino 1 Comment

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

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Posted in: Linear Algebra

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