# Linear Algebra

Linear algebra is the branch of mathematics concerning linear equations, linear maps, and their representations in vector spaces and through matrices.

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as basically the application of linear algebra to spaces of functions.

Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.

from Linear Algebra - Wikipedia

This topic includes the following resources and journeys:

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## Linear Algebra Review

Intermediate
Course
Theory

This short course is a quick review of linear algebra, intended for students who have already taken a previous course in linear algebra or have some experience with vectors and matrices. The...

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## Linear Systems of Equations, Least Squares Regression, Pseudoinverse

11 min
Beginner
Video
Theory

This video describes how the SVD can be used to solve linear systems of equations. In particular, it is possible to solve nonsquare systems (overdetermined or underdetermined) via least...

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## Finding Roots of a Polynomial Using Matlab, Mathematica, and a TI-83

10 min
Beginner
Video
Application

In this video we show how to use Matlab and Mathematica to solve for roots of an arbitrary order polynomial. For fun, we also show how an old graphing calcu...

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## Linear Systems of Equations

10 min
Beginner
Video
Theory

This video describes linear systems of equations and when they have solutions.

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## Gaussian/Normal Distributions

99 min
Beginner
Video
Theory

In this video we discuss the Gaussian (AKA Normal) probability distribution function. We show how it relates to the error function (erf) and discuss how to ...

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## Inner Products in Hilbert Space

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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## Unitary Transformations

12 min
Beginner
Video
Theory

This video discusses unitary matrix transformations and how they relate to the geometry of the singular value decomposition (SVD).

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## Cayley-Hamilton Theorem [Control Bootcamp]

6 min
Beginner
Video
Theory

Here we describe the Cayley-Hamilton Theorem, which states that every square matrix satisfies its own characteristic equation. This is very useful to prove results related to...

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## The Frobenius Norm for Matrices

2 min
Intermediate
Video
Theory

This video describes the Frobenius norm for matrices as related to the singular value decomposition (SVD).

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## Essence of Linear Algebra: Understand the Geomterical Beauty in Linear Algeb...

140 min
Intermediate
Course
Application

Linear Algebra is a very important and fundamental topic needed in almost every field of STEM. While the linear part of it is easy to understand and perform operations on, the geometric...

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## Matrix Completion and the Netflix Prize

6 min
Beginner
Video
Theory

This video describes how the singular value decomposition (SVD) can be used for matrix completion and recommender systems.

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## crash course on complex numbers

10 min
Beginner
Video
Theory

In this video, we quickly review “Complex Numbers”. The following materials are covered:1- Cartesian and polar representation of complex numbers2- how to con...

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