matrix_operations/

README

Matrix Operations, Linear Algebra

As mentioned, matrix operations are ubiquitous in the data science world. Most machine learning algorithms and many statistical/modeling techniques rely on iterative matrix operations including solving for eigenvalues/vectors, finding determinants, taking transposes, and more. We will highlight a few here, such that you can have confidence in implementing your own custom models and understand various pre-existing implementations.

Notes

• Matrix multiplication is in general not commutative.
• Many of the familiar rules for arithmetic with numbers hold in the case of matrix arithmetic.
• "Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, proper vectors, or latent vectors... Each eigenvector is paired with a corresponding so-called eigenvalue" from Wolfram Mathworld.
• A norm is a function that assigns a strictly positive length or size to a vector or matrix.

Links

gonum.org/v1/gonum/mat docs
The Matrix Cookbook
Khan Academy - Matrices
Khan Academy - Linear Algebra
Eigenvalues and eigenvectors explained visually

Code Review

Matrix arithmetic
Transpose, Det, Dot Product, Inverse
Solve for eigenvalues/vectors
Vector/Matrix Norms

Exercises

Exercise 1

Divide the following matrix by its norm:

a = ⎡1  2  3⎤
    ⎢0  4  5⎥
    ⎣0  0  6⎦

Template | Answer

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All material is licensed under the Apache License Version 2.0, January 2004.