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
%}
Methods of Solving Linear Equations
- Gaussian Elimination : gaussian elimination is one the primary methods
for solving a system of equations as above.
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 representation of a given 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 indpedently.
Additional Topics
Linear Algebra API
