Linear Algebra/Index

A

accuracy

of Gauss' method

addition

vector

additive inverse

adjoint matrix

angle

antipodal

antisymmetric matrix

argument

Arithmetic-Geometric Mean Inequality

arrow diagram 1, 2, 3, 4, 5

augmented matrix

automorphism

dilation

reflection

rotation

B

back-substitution

base step

of induction

basis 1, 2, 3

change of

definition

natural

orthogonal

orthogonalization

orthonormal

standard 1, 2

standard over the complex numbers

string

best fit line

binary relation

block matrix

box

orientation

sense

volume

C

C language

classes

equivalence

canonical form

for row equivalence

for matrix equivalence

for nilpotent matrices

for similarity

canonical representative

Cauchy-Schwarz Inequality

Caley-Hamilton theorem

change of basis

characteristic

equation

polynomial

value

vector

characterized

Chemistry problem 1, 2, 3

central projection

circuits

parallel

series

series-parallel

closure

of rangespace

of nullspace

codomain

cofactor

column

vector

column rank

full

column space

complement

complementary subspaces

orthogonal

complex numbers

vector space over

component

composition

self

computer algebra systems

concatenation

condition number

congruent figures

congruent plane figures

contradiction

contrapostivite

convex set

coordinates

homogeneous

with respect to a basis

corollary

correspondence 1, 2

cosets

Cramer's Rule

cross product

crystals

diamond

graphite

salt

unit cell

D

da Vinci, Leonardo

determinant 1, 2

cofactor

Cramer's Rule

definition

exists 1, 2, 3

Laplace Expansion

minor

Vandermonde

permutation expansion 1, 2

diagonal matrix 1, 2

diagonalizable

difference equation

homogeneous

dilation

matrix representation

dimension

physical

dilation 1, 2

direct map

direct sum

definition

of two subspaces

external

internal

direction vector

distance-preserving

division theorem

domain

dot product

double precision

dual space

E

echelon form

leading variable

free variable

reduced

eigenvalue

of a matrix

of a transformation

eigenvector

of a matrix

of a transformation

eigenspace

element

elementary

matrix

elementary reduction matrices

elementary reduction operations

pivoting

rescaling

swapping

elementary row operations

empty

Erlanger Program

entry

equivalence

class

canonical representative

representitive

equivalence relation 1, 2

row equivalence

isomorphism

matrix equivalence

matrix similarity

equivalent statements

Euclid

even functions 1, 2

even polynomials

external direct sum

F

Fibonacci sequence

field

definition

finite-dimensional vector space

flat

form

free variable

full column rank

full row rank

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

Gauss' Method

accuracy

back-substitution

elementary operations

Gauss-Jordan

Gauss-Jordan

Gaussian operations

generalized nullspace

generalized rangespace

Gram-Schmidt Orthogonalization

Geometry of Eigenvalues

Geometry of Linear Maps

H

historyless

Markov Chain

homogeneous

homogeneous coordinate vector

homogeneous coordinates

homorphism

composition

matrix representation 1, 2, 3

nonsingular 1, 2

nullity

nullspace

rank 1, 2

rangespace

rank

zero

I

ideal line

ideal point

identity function

identity matrix 1, 2

identity function

if-then statement

ill-conditioned

image

under a function

improper subspace

incidence matrix

index

of nilpotentcy

induction 1, 2

inductive step

of induction

inherited operations

inner product

Input-Output Analysis

internal direct sum 1, 2

intersection

invariant subspace

definintion

inverse

additive

left inverse

matrix

right inverse

two-sided

inverse function

inverse image

inversion

isometry

isomorphism 1, 2, 3

characterized by dimension

definition

of a space with itself

J

Jordon form

represents similarity classes

Jordon block

K

kernel

Kirkoff's Laws

Klein, F.

L

Laplace Expansion

leading variable

least squares

lemma

length

Leontief, W.

line

at infinity

in projective plane

of best fit

linear

tranpose operation

linear combination

Linear Combination Lemma

linear equation

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

linear recurrence

linear relationship

linear surface

linear transformation

linearly dependent

linearly independent

LINPACK

M

map

extended linearly

distance-preserving

self composition

Maple

Markov Chain

historyless

Markov matrix

material implication

Mathematica

mathematical induction1, 2

MATLAB

matrix

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

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

matrix equivalence

definition

cononical form

rank characterization

mean

arithmetic

geometric

member

method of powers

minimal polynomial 1, 2

minor

morphism

multilinear

multiplication

matrix-matrix

matrix-vector

MuPAD

mutual inclusion 1, 2

N

natural representative

networks

Kirkoff's Laws

nilpotent

canonical form for

definition

matrix

transformation

nilpotentcy

index

nonsingular

homomorphism

matrix

normalize

nullity

nullspace

closure of

generalized

O

Octave

odd functions 1, 2

odd polynomials

one-to-one function

onto function

opposite map

order of a recurrence

ordered pair

orientation 1, 2

orthogonal

basis

complement

mutually

projection

matrix

orthogonalization

orthonormal basis

orthonormal matrix

P

pair

ordered

parallelepiped

parallelogram rule

parameter

partition

matrix equivalence classes

partial pivoting

partitions

row equivalence classes

isomorphism classes

matrix equivalence classes

Pascal's triangle

permutation

inversions

matrix

signum

permutation expansion 1, 2

perp

perpendicular

permutation expansion

perspective

triangles

Physics problem

pivoting

on rows

full

partial

scaled

plane figure

congruence

polynomial

division theorem

even

odd

of a map

of a matrix

minimal

point

at infinity

in the projective plane

populations, stable

potential

powers, method of

preserves structure

probability vector

projection 1, 2, 3, 4

along a subspace

central

vanishing point

onto a line

onto a subspace

orthogonal 1, 2

Projective Geometry

projective plane

Duality Principle

ideal line

ideal points

lines

proof techniques

induction

proper

subspace

subset

propositions

equivalent

Q

quantifier 1, 2

existential

universal

R

range

rangespace

closure of

generalized

rank 1, 2

column

of a homomorphism 1, 2

row

recurrence 1, 2

homogeneous

initial conditions

reduced echelon form

reflection

glide

reflection about a line

matrix representation

reflexivity

relation

equivalence

reflexive

symmetric

transitive

relationship

linear

representation

of a vector

of a matrix

representative

canonical

for row equivalence

of matrix equivalence classes

of similarity classes

rescaling rows

resistance

equivalent

resistor

restriction

rigid motion

rotation 1, 2, 3

matrix representation

rounding error

row

vector

row equivalence

row rank

full

row space

S

scaled partial pivoting

scalar

scalar multiple

matrix

vector

scalar multiplication

vector 1, 2

scalar product

Schur's triangularization lemma

Schwarz Inequality

SciLab

self composition

of maps

sense

sequence

concatenation

set

complement

element

empty

empty

intersection

linearly dependent

linearly independent

member

mutual inclusion 1, :2

proper subset

span of

subset

union

signum

similar 1, 2, 3

canonical form

similar triangles

similarity transformation

single precision

singular

matrix

size 1, 2

sgn

see signum

skew

skew-symmetric

span

of a singleton

spin

square root

stable populations

standard basis

state

absorbing

Statics problem

string

basis

of basis vectors

structure

preservation

submatrix

subset

subspace

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

swapping rows

symmetric matrix 1, 2, 3, 4

symmetry

system of linear equations

Gauss' Method

solving

T

theorem

trace 1, 2, 3

transformation

characteristic polynomial

composed with itself

diagonalizable

eigenvalue

eigenvector

eigenspace

Jordon form

minimal polynomial

nilpotent

canonical representative

projection

size change

transition matrix

transitivity

translation

transpose 1, 2

interaction with sum and scalar multiplication

determinant 1, 2

triangles

similar

Triangle Inequality

triangular matrix

triangularization

trivial space 1, 2

turning map

matrix representation

U

union

unit matrix

V

vacuously true

value

Vandermonde

determinant

matrix

vanishing point

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

vector space

basis

definition 1, 2

dimension

dual

finite-dimensional

homomorphism

isomorphism

map

over complex numbers

subspace

trivial 1, 2

Venn diagram

voltage drop

volume

voting paradox:

majority cycle

rational preference

spin

voting paradoxes

W

Wheatstone bridge

well-defined

Z

zero divisor 1, 2

zero homomorphism

zero vector 1, 2