We just looked at some simple ways to solve systems of differential equations, via modeling and elimination. But there are other methods, some of which involve matrices. This will require that we remember some concepts from linear...

We've learned about matrix diagonalization, which is a type of matrix decomposition. There are some others that we must learn, including LU decomposition, Cholesky decomposition, QR decomposition, and singular value decomposition. Let's...

These second-order linear differential equations can be written in the form dx/dt = ax + by dy/dt = cx + dy Depending on the values of a,b,c and d, the dynamics will be very different! They can be characterized by finding the eigenvalues...

These second-order linear differential equations can be written in the form

dx/dt = ax +
by
dy/dt =
cx + dy
Depending on the values of a,b,c and d, the dynamics will be very different! They can be...

I made a (free) linear algebra tool - What I use to make my videos

Performing diagonalization.

Postulates of Quantum Mechanics: Eigenvalues & Eigenfunctions

In this video, we will cover Singular Value Decomposition (SVD).
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning...

In this video, we will cover PCA versus SVD.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and...

In this video, we will cover PCA for small sample size problems (DualPCA).
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine...

In this video, we will cover PCA derivation.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and...

In this video, we will cover a positive semi definite matrix.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning...

In this video, we will cover Lagrange Multipliers.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and...

Defining eigenvalues and eigenvectors, and outlining how to solve for them given a particular matrix.