Linear Algebra
Overview
Linear Algebra is the field of mathematics that deals with solving systems linear equations, such as the following.
{%
a_{11} x_1 + a_{12} x_2 + a_{13} x_3 + ... + a_{1n} x_n = b_1 \\
a_{21} x_1 + a_{22} x_2 + a_{23} x_3 + ... + a_{2n} x_n = b_2 \\
... \\
a_{n1} x_1 + a_{n2} x_2 + a_{n3} x_3 + ... + a_{nn} x_n = b_1
%}
Gaussian Elimination is one the primary methods
for solving a system of equations as above, which helped to lay the foundations of linear algebra.
Theory
As mathematicians began to develop the tools necessary to solve systems of equations, as above, the theory underpinning linear algebra began to emerge. The broad categories of the theory can be enumerated as the following:- Vector spaces - the fundamental underpinning of linear algebra, linear transformation (or matrix) represents a linear mapping from one vector space to another
- Linear Transformations
- Matrices : are a representation of a linear transformation given a set of bases for the domain and range of the transformation. However, matrices are mathematical objects in their own right, which can studied independently.
Linear Algebra API
- Linear Algebra API : library for doing linear algebra calculations
- Matrix API : library for doing linear algebra calculations (object based)
- Linear Algebra for Complex Numbers API : library for doing linear algebra calculations
- Linear Algebra with TensorFlow.js
- Gpu Accelerated Linear Algebra - library for running matrix operations on the GPU if available.