Linear Algebra Tags

# Linear Algebra Tags

## Systems of linear equations

- Systems with 2 variables
- Systems with 3 variables
- Systems with 4 or more variables
- Matrix-vector forms
- Vector equations
- Augmented matrices

## Matrices

- Matrix basics
- Matrix algebra
- Row operations
- Echelon form
- Rank
- Transpose and trace
- Inverses
- Elementary matrices
- Complex entries
- Markov chains

## Matrix factorizations

- Diagonalization
- LU factorization
- QR factorization
- Singular value decomposition
- Jordan form

## Euclidean spaces

- Vectors
- Linear combinations
- Span
- Linear independence
- Subspaces
- Basis and dimension
- Row, column, and null spaces
- Coordinate vectors and change of basis

## Vector geometry

- Vectors and vector arithmetic
- Dot product, length, and unit vectors
- Cross product
- Planes
- Lines with planes
- Coordinate systems

## Abstract vector spaces

- Definition and properties
- Linear combinations
- Span
- Linear independence
- Subspaces
- Basis and dimension
- Coordinate vectors and change of basis
- Examples

## Eigenvalues and eigenvectors

- Computing eigenvalues and eigenvectors
- Properties
- Complex eigenvalues and eigenvectors
- Quadratic forms

## Inner products

- Computing with dot products
- Computing with inner products
- Orthogonal and orthonormal sets
- Projection and distance
- Gram-Schmidt process
- Orthogonal matrices

## Linear transformations

- Evaluating linear transformations
- Associated matrices
- One-to-one and onto
- Kernel and image
- Inverses

## Determinants

- Computing determinants
- Properties
- Applications