Linear Algebra/Index

< Linear Algebra

A

accuracy

of Gauss' method

addition

additive inverse

antisymmetric matrix

Arithmetic-Geometric Mean Inequality

arrow diagram 1, 2, 3, 4, 5

augmented matrix

B

back-substitution

base step

basis 1, 2, 3

orthogonalization

standard 1, 2

standard over the complex numbers

binary relation

C

classes

canonical form

for row equivalence

for matrix equivalence

for nilpotent matrices

canonical representative

Cauchy-Schwarz Inequality

Caley-Hamilton theorem

change of basis

characteristic

Chemistry problem 1, 2, 3

central projection

circuits

series-parallel

complementary subspaces

complex numbers

vector space over

computer algebra systems

condition number

congruent figures

congruent plane figures

contrapostivite

coordinates

with respect to a basis

correspondence 1, 2

D

da Vinci, Leonardo

determinant 1, 2

exists 1, 2, 3

Laplace Expansion

permutation expansion 1, 2

diagonal matrix 1, 2

difference equation

dilation

matrix representation

dilation 1, 2

of two subspaces

direction vector

distance-preserving

division theorem

double precision

E

leading variable

eigenvalue

of a transformation

eigenvector

of a transformation

elementary

elementary reduction matrices

elementary reduction operations

elementary row operations

Erlanger Program

equivalence

canonical representative

equivalence relation 1, 2

row equivalence

matrix equivalence

matrix similarity

equivalent statements

even functions 1, 2

even polynomials

external direct sum

F

Fibonacci sequence

finite-dimensional vector space

full column rank

function 1, 2

inverse 1, 2

one-to-one function

structure preserving 1, 2

see homomorphism

two sided inverse

Fundamental Theorem

of Linear Algebra

G

back-substitution

elementary operations

Gaussian operations

generalized nullspace

generalized rangespace

Gram-Schmidt Orthogonalization

Geometry of Eigenvalues

Geometry of Linear Maps

H

historyless

homogeneous coordinate vector

homogeneous coordinates

matrix representation 1, 2, 3

nonsingular 1, 2

rank 1, 2

I

identity function

identity matrix 1, 2

identity function

if-then statement

ill-conditioned

image

under a function

improper subspace

incidence matrix

index

induction 1, 2

inductive step

inherited operations

Input-Output Analysis

internal direct sum 1, 2

invariant subspace

inverse function

isomorphism 1, 2, 3

characterized by dimension

of a space with itself

J

represents similarity classes

K

M

extended linearly

distance-preserving

self composition

material implication

mathematical induction1, 2

block 1, 2

change of basis

characteristic polynomial

condition number

determinant 1, 2

diagonal matrix 1, 2

elementary reduction 1, :2

identity 1, 2

inverse 1, 2

minimal polynomial

scalar multiple

symmetric 1, 2, 3,4, 5, 6

trace 1, 2, 3

transpose 1, 2, 3

matrix-vector product

minimal polynomial

nonsingular 1, 2

principle diagonal

row equivalence

scalar multiple

symmetric 1, 2, 3,4, 5

trace 1, 2

transpose 1, 2, 3

triangular 1, 2, 3

matrix equivalence

rank characterization

mean

method of powers

minimal polynomial 1, 2

multiplication

mutual inclusion 1, 2

N

natural representative

canonical form for

nilpotentcy

O

odd functions 1, 2

odd polynomials

one-to-one function

order of a recurrence

orientation 1, 2

orthogonalization

orthonormal basis

orthonormal matrix

P

pair

parallelogram rule

matrix equivalence classes

partial pivoting

partitions

row equivalence classes

isomorphism classes

matrix equivalence classes

Pascal's triangle

permutation expansion 1, 2

permutation expansion

perspective

Physics problem

pivoting

polynomial

division theorem

point

in the projective plane

populations, stable

powers, method of

preserves structure

probability vector

projection 1, 2, 3, 4

along a subspace

vanishing point

onto a subspace

orthogonal 1, 2

Projective Geometry

projective plane

Duality Principle

proof techniques

proper

Q

quantifier 1, 2

R

rank 1, 2

of a homomorphism 1, 2

recurrence 1, 2

initial conditions

reduced echelon form

reflection about a line

matrix representation

relationship

representation

for row equivalence

of matrix equivalence classes

of similarity classes

rotation 1, 2, 3

matrix representation

row equivalence

S

scaled partial pivoting

scalar multiple

scalar multiplication

vector 1, 2

Schur's triangularization lemma

Schwarz Inequality

self composition

linearly dependent

linearly independent

mutual inclusion 1, :2

similar 1, 2, 3

similar triangles

similarity transformation

single precision

singular

size 1, 2

sgn

stable populations

Statics problem

of basis vectors

structure

orthogonal complement

sum

vector 1, 2, 3, 4

summation notation

for permutation expansion

symmetric matrix 1, 2, 3, 4

system of linear equations

T

trace 1, 2, 3

transformation

characteristic polynomial

composed with itself

minimal polynomial

canonical representative

transition matrix

transpose 1, 2

interaction with sum and scalar multiplication

determinant 1, 2

triangles

Triangle Inequality

triangular matrix

triangularization

trivial space 1, 2

matrix representation

U

V

Vandermonde

vanishing point

vector 1, 2

angle between vecots

canonical position

complex scalars

homogeneous coordinate

natural position

representation of 1, 2

satisfies an equation

scalar multiple

scalar multiplication 1, 2

sum 1, 2, 3, 4

zero vector 1, 2

definition 1, 2

finite-dimensional

over complex numbers

trivial 1, 2

voting paradox:

rational preference

voting paradoxes

W

Wheatstone bridge

X

Y

Z

zero divisor 1, 2

zero homomorphism

zero vector 1, 2

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