PX153 - K0 - outline

matrices are arrays of numbers that appear naturally in:
- systems of linear equations
- modelling of dynamical systems, best linear approximation, that can be expressed as simultaneous linear equations (eg: coupled pendulums)
- quantum mechanics
- computational physics
outline:
- inverse matrix
  - for a matrix, $A$ , its inverse, such that, $A A^{- 1} = I$ , where $I$ is an identity matrix
- eigenvalues and eigenvectors
  - $A \vec{x} = λ \vec{x}$ , where $\vec{x}$ and $λ$ are the eigenvector and eigenvalue respectively
- the effect of a matrix, $A$ , on a vector space, ${\vec{x}}$
  - $A$ can be thought as a map going from ${x}$ to ${y}$