# Linear Algebra/Index

Contents: Top - 0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

## A

accuracy

of Gauss' method

vector

arrow diagram 1, 2, 3, 4, 5

dilation
reflection
rotation

## B

base step

of induction

basis 1, 2, 3

change of
definition
natural
orthogonal
orthogonalization
orthonormal
standard 1, 2
standard over the complex numbers
string
orientation
sense
volume

## C

classes

equivalence

canonical form

for row equivalence
for matrix equivalence
for nilpotent matrices
for similarity

characteristic

equation
polynomial
value
vector

Chemistry problem 1, 2, 3

circuits

parallel
series
series-parallel
of rangespace
of nullspace
vector
full
orthogonal

complex numbers

vector space over
self

coordinates

homogeneous
with respect to a basis

correspondence 1, 2

diamond
graphite
salt
unit cell

## D

determinant 1, 2

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

diagonal matrix 1, 2

homogeneous

dilation

matrix representation
physical

dilation 1, 2

definition
of two subspaces
external
internal
dual space

## E

free variable
reduced

eigenvalue

of a matrix
of a transformation

eigenvector

of a matrix
of a transformation

elementary

matrix
pivoting
rescaling
swapping

equivalence

class
canonical representative
representitive

equivalence relation 1, 2

row equivalence
isomorphism
matrix equivalence
matrix similarity

even functions 1, 2

## F

definition

function 1, 2

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
see homomorphism
two sided inverse
value
well-defined
zero

Fundamental Theorem

of Linear Algebra

## G

accuracy
back-substitution
elementary operations
Gauss-Jordan

## H

historyless

Markov Chain
composition
matrix representation 1, 2, 3
nonsingular 1, 2
nullity
nullspace
rank 1, 2
rangespace
rank
zero

## I

identity matrix 1, 2

image

under a function

index

of nilpotentcy

induction 1, 2

inductive step

of induction

internal direct sum 1, 2

definintion
left inverse
matrix
right inverse
two-sided

isomorphism 1, 2, 3

characterized by dimension
definition
of a space with itself

## J

represents similarity classes

## L

line

at infinity
in projective plane
of best fit

linear

tranpose operation
coefficients
constant
homogeneous
solution of
Cramer's Rule
Gausses' Method
Gauss-Jordan
system of
satisfied by a vector

linear map

dilation
see homomorphism
reflection
rotation 1, 2
skew
trace

## M

extended linearly
distance-preserving
self composition
historyless

mathematical induction1, 2

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
existence
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
definition
cononical form
rank characterization

mean

arithmetic
geometric

minimal polynomial 1, 2

multiplication

matrix-matrix
matrix-vector

mutual inclusion 1, 2

## N

Kirkoff's Laws
canonical form for
definition
matrix
transformation

nilpotentcy

index
homomorphism
matrix
closure of
generalized

## O

odd functions 1, 2

order of a recurrence

orientation 1, 2

basis
complement
mutually
projection
matrix

## P

pair

ordered
matrix equivalence classes

partitions

row equivalence classes
isomorphism classes
matrix equivalence classes
inversions
matrix
signum

permutation expansion 1, 2

perspective

triangles

pivoting

on rows
full
partial
scaled
congruence

polynomial

division theorem
even
odd
of a map
of a matrix
minimal

point

at infinity
in the projective plane

projection 1, 2, 3, 4

along a subspace
central
vanishing point
onto a line
onto a subspace
orthogonal 1, 2

projective plane

Duality Principle
ideal line
ideal points
lines

proof techniques

induction

proper

subspace
subset
equivalent

quantifier 1, 2

existential
universal

## R

closure of
generalized

rank 1, 2

column
of a homomorphism 1, 2
row

recurrence 1, 2

homogeneous
initial conditions
glide
matrix representation
equivalence
reflexive
symmetric
transitive

relationship

linear

representation

of a vector
of a matrix
canonical
for row equivalence
of matrix equivalence classes
of similarity classes
equivalent

rotation 1, 2, 3

matrix representation
vector
full

## S

scalar multiple

matrix
vector

scalar multiplication

vector 1, 2

self composition

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

similar 1, 2, 3

canonical form

singular

matrix

size 1, 2

sgn

see signum
of a singleton
absorbing
basis
of basis vectors

structure

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

sum

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

summation notation

for permutation expansion

symmetric matrix 1, 2, 3, 4

Gauss' Method
solving

## T

trace 1, 2, 3

transformation

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

transpose 1, 2

interaction with sum and scalar multiplication
determinant 1, 2

triangles

similar

trivial space 1, 2

matrix representation

## V

Vandermonde

determinant
matrix

vector 1, 2

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
majority cycle
rational preference
spin

## Z

zero divisor 1, 2

zero vector 1, 2