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