# Linear Algebra/Index

## A

editaccuracy

addition

## B

editbase step

## C

editclasses

canonical form

characteristic

circuits

complex numbers

coordinates

## D

edit- cofactor
- Cramer's Rule
- definition
- exists 1, 2, 3
- Laplace Expansion
- minor
- Vandermonde
- permutation expansion 1, 2

dilation

## E

editeigenvalue

eigenvector

elementary

elementary reduction operations

equivalence

## F

editfinite-dimensional vector space

- argument
- codomain
- composition
- composition
- correspondence
- domain
- even
- identity
- inverse 1, 2
- inverse image
- left inverse
- multilinear
- range
- restriction
- odd
- one-to-one function
- onto
- right inverse
- structure preserving 1, 2
- two sided inverse
- value
- well-defined
- zero

Fundamental Theorem

## G

edit## H

edithistoryless

## I

editimage

index

inductive step

## J

edit## K

edit## L

editline

linear

linear map

- dilation
- see homomorphism
- reflection
- rotation 1, 2
- skew
- trace

## M

edit- adjoint
- antisymmetric
- augmented
- block 1, 2
- change of basis
- characteristic polynomial
- cofactor
- column
- column space
- condition number
- determinant 1, 2
- diagonal matrix 1, 2
- diagonalizable
- diagonalized
- eigenvalue
- eigenvector
- elementary reduction 1, :2
- entry
- equivalent
- form
- identity 1, 2
- incidence
- inverse 1, 2
- left inverse
- main diagonal
- Markov
- minimal polynomial
- minor
- nilpotent
- nonsingular
- orthogonal
- orthonormal
- right inverse
- scalar multiple
- skew-symmetric
- similar
- similarity
- singular
- submatrix
- sum
- symmetric 1, 2, 3,4, 5, 6
- trace 1, 2, 3
- transition
- transpose 1, 2, 3
- Markov
- matrix-vector product
- minimal polynomial
- multiplication
- nonsingular 1, 2
- permutation
- principle diagonal
- rank
- representation
- row
- row equivalence
- row rank
- row space
- scalar multiple
- singular
- sum
- symmetric 1, 2, 3,4, 5
- trace 1, 2
- transpose 1, 2, 3
- triangular 1, 2, 3
- unit
- Vandermonde

mean

multiplication

## N

editnilpotentcy

## O

editorder of a recurrence

## P

editpair

partitions

perspective

pivoting

polynomial

point

- along a subspace
- central
- onto a line
- onto a subspace
- orthogonal 1, 2

projective plane

proof techniques

proper

## Q

edit## R

editrelationship

representation

## S

editscalar multiple

scalar multiplication

Schur's triangularization lemma

self composition

- complement
- element
- empty
- empty
- intersection
- linearly dependent
- linearly independent
- member
- mutual inclusion 1, :2
- proper subset
- span of
- subset
- union

singular

sgn

structure

- closed
- complementary
- direct sum
- definition
- improper
- independence
- invariant
- orthogonal complement
- proper
- sum

sum

- of matrices
- of subspaces
- vector 1, 2, 3, 4

summation notation

## T

edittransformation

- characteristic polynomial
- composed with itself
- diagonalizable
- eigenvalue
- eigenvector
- eigenspace
- Jordon form
- minimal polynomial
- nilpotent
- projection
- size change

- interaction with sum and scalar multiplication
- determinant 1, 2

triangles

## U

edit## V

editVandermonde

- angle between vecots
- canonical position
- closure
- column
- complex scalars
- component
- cross product
- direction
- dot product
- free
- homogeneous coordinate
- length
- natural position
- orthogonal
- probability
- representation of 1, 2
- row
- satisfies an equation
- scalar multiple
- scalar multiplication 1, 2
- sum 1, 2, 3, 4
- unit
- zero vector 1, 2

- basis
- definition 1, 2
- dimension
- dual
- finite-dimensional
- homomorphism
- isomorphism
- map
- over complex numbers
- subspace
- trivial 1, 2