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Numerically Linearizing a Dynamic System

Christopher Lum
104 min
Intermediate
Video
Theory

In this video we show how to linearize a dynamic system using numerical techniques. In other words, the linearization process does not require an analytical description of the system. This...

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Data-Driven Control: Balanced Models with ERA

Steve Brunton
6 min
Intermediate
Video
Theory

In this lecture, we connect the eigensystem realization algorithm (ERA) to balanced proper orthogonal decomposition (BPOD). In particular, if enough data is collected, then ERA produces...

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Inner Products in Hilbert Space

Steve Brunton
8 min
Intermediate
Video
Theory

This video will show how the inner product of functions in Hilbert space is related to the standard inner product of vectors of data.

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Dynamic Mode Decomposition (Code)

Steve Brunton
8 min
Intermediate
Video
Application

In this video, we code up the dynamic mode decomposition (DMD) in Matlab and use it to analyze the fluid flow past a circular cylinder at low Reynolds number.

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Linear Regression 1 [Matlab]

Steve Brunton
12 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used for linear regression in Matlab (part 1).

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Parseval's Theorem

Steve Brunton
5 min
Intermediate
Video
Theory

Parseval's theorem is an important result in Fourier analysis that can be used to put guarantees on the accuracy of signal approximation in the Fourier domain.

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SVD: Eigenfaces 1 [Python]

Steve Brunton
4 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Python code, part 1).

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