A
abelian group
adjoint of a matrix
adjugate of a matrix
algebraic multiplicity of eigenvalues
antihermitian matrix
antisymmetric matrix
B
basis
bidiagonal matrix
bisymmetric matrix
block matrix
|_ determinant; inverse
block-diagonal matrix
C
caley formulae
|_ complex; real
Cauchy-Schwartz inequality
|_
cayley-hamilton theorem
centrohermitian matrix
centrosymmetric matrix
chain rule for derivatives
characteristic
|_ equation; of field or integral domain; polynomial
cholesky decomposition
circulant matrix
circular matrix
cofactor
companion matrix
complex
|_ derivative; Gaussian vector; gradient; matrix
Complex-to-Real isomorphism
compound matrix
condition number
Conditional Gaussian distribution
congruent matrices
conjugate
|_ derivative; matrices
conjunctive matrices
constrained minimization
constructibility
controllability
convergent matrix
convolution identities
correlation coefficient
|_ matrix
|_
Courant-Fischer theorem
covariance matrix
Cramer-Rao bound
cross product
Cyclic
|_ Permutation Matrix; Shift Matrix
D
decomposable matrix
decomposition
|_ cholesky; ldu; lu; polar; qr
|_ schur
| |_ generalised
| |_ real
| |_ generalised
|_ singular value
defective
|_ eigenvalue; matrix
definitness of a matrix
departure from normality
derivative
|_ chain rule; complex; conjugate
|_ of
|_ cubic product; determinant; inverse; linear product
|_ quadratic product; trace
derogatory matrix
detectability
determinant
|_ derivative of; lemma
|_ of
|_ block matrices; product; simple matrices; sum
dft : discrete fourier transform
diagonable matrix
diagonal matrix
diagonalisation of two matrices
diagonalizable matrix
diagonally dominant matrix
differential entropy
dimension
direct sum
discrete fourier transform
displacement rank
doubly stochastic matrix
Durbin recursion
E
eigenspace
eigenvalue
|_ defective; regular; simple
eigenvalues of a matrix
eigenvector
entropy
equivalence relation
equivalent matrices
essential matrix
euclidean norm
|_ matrix; vector
exchange matrix
expected value of
|_ 1:linear expressions
|_ 2:quadratic expressions
| |_ minimizing quadratic expressions
|_ 3:cubic expressions; 4:quartic expressions
|_ 5:quintic expressions; higher powers
F
fast fourier transform
fft: fast fourier transform
field of values
field, formal definition
Finite Field
Fisher
|_ Information matrix; Score vector
fourier transform
|_ discrete; fast
frobenius matrix norm
functions
|_ SKEW
G
Galois Field
Gaussian
|_ conditional distribution; multiple correlation coefficient
|_ power; precision matrix; product; quotient
|_ vector
|_ complex; real
generalised inverse
geometric multiplicity of eigenvalues
Givens
|_ reflection; rotation
gradient complex
gram matrix
gram-schmitt orthogonalization
grammian of a matrix
group, formal definition
H
hadamard
|_ inequality
| |_ generalised
|_ product
hankel matrix
hermite normal form
hermitian
|_ matrix
| |_ partial order
|_ transpose
hessenberg matrix
hessian matrix
Hilbert-Schmidt matrix norm
holder
|_ inequality; norm
homogeneous
|_ matrix; vector
householder matrix
hypercompanion matrix
I
idempotent matrix
identity matrix
image
impotent
incidence matrix
indefinite matrix
induced matrix norm
inertia
|_ matrix
inner product
|_ norm
integral domain
inverse
|_ derivative of; generalised; moore-penrose; of block matrix
|_ pseudoinverse
inversion
|_ lemma; sums
involutary matrix
irreducible matrix
Isomorphism Complex-to-Real
Isserlis' therem
J
jacobi matrix
jacobian
jordan normal form
K
k'th root of Hermitian matrix
kernel
kronecker
|_ delta; product; sum
L
Lagrange multipliers
LDU decomposition
lemma
|_ matrix_determinant; matrix_inversion
linear
|_ discriminant analysis
|_ equation
| |_ least squares
| |_ recursive
|_ independence
|_ formal definition
loewner partial order
lower shift matrix
LU decomposition
lyapunov matrix equation
|_ continuous; discrete
M
matrix
|_ determinant lemma
|_ equation
| |_ linear
| |_ lyapunov
| | |_ continuous; discrete
| |_ riccati
| | |_ continuous; discrete
| |_ sylvester
|_ inversion lemma; norm
|_ types
|_ antihermitian; antisymmetric; bidiagonal; bisymmetric
|_ block_diagonal; centrohermitian; centrosymmetric
|_ circulant; circular; companion; complex; convergent
|_ decomposable; defective; definite; derogatory; diagonal
|_ diagonalizable; diagonally dominant; doubly_stochastic
|_ exchange; givens_reflection; givens_rotation; hadamard
|_ hamiltonian; hankel; hermitian; hessenberg; hilbert
|_ householder; hypercompanion; idempotent; identity
|_ incidence; indefinite; integral; involutary; jacobi
|_ monotone; nilpotent; non-negative; normal; orthogonal
|_ permutation; perplectic; persymmetric; polynomial
|_ positive; positive_definite; primitive; projection
|_ quaternion; rank-one; reducible; regular; rotation
|_ signature; simple; singular; skew-hermitian
|_ skew-symmetric; sparse; stability; stochastic
|_ subunitary; symmetric; symmetric_centrosymmetric
|_ symmetrizable; symplectic; toeplitz; triangular
|_ tridiagonal; unitary; vandermonde; vectorized transpose
|_ zero
maximization of Quadratic Form
minimization of trace
minkowski inequality
minor
|_ cofactor of; principal
monotone matrix
Moore-Penrose inverse
multiple correlation coefficient
multiplicity of eigenvalues
|_ algebraic; geometric
N
natural inverse
negative definite matrix
nilpotent matrix
non-negative matrix
norm
|_ formal definition
|_ matrix
| |_ euclidean; frobenius; Hilbert-Schmidt; p
|_ vector
|_ euclidean; holder; p
normal matrix
normality, departure from
null space
nullity
O
observability
Optimization of Quadratic Form
orthogonal matrix
orthogonalization, gram-schmitt
orthogonally similar matrices
P
p-norm
|_ matrix; vector
parallelogram identity
parseval's theorem
permanent of a matrix
perplectic matrix
perron's theorem
perron-frobenius theorem
persymmetric matrix
polar factorisation
positive
|_ definite matrix; matrix; semi-definite matrix
potency
Power of Gaussian pdf
precision matrix
Product of Gaussian pdfs
projection matrix
|_ identities
projective space
pseudoinverse
Q
QR decomposition
Quadratic Form Optimization
quaternion
Quotient of Gaussian pdfs
R
range
rank
rank-one matrix
Rayleigh-Ritz theorem
reachability
real Gaussian vector
recursive least squares
reducible matrix
reflection householder
regression coefficient matrix
regular
|_ eigenvalue; matrix
riccati matrix equation
|_ continuous; discrete
ring
rotation matrix
|_ givens
row echelon form
S
Schur
|_ complement
|_ decomposition
| |_ generalised
| | |_ real
| |_ real
|_ product
Sherman-Morrison formula
shift matrix
signature matrix
similar matrices
simple
|_ eigenvalue; matrix
singular
|_ matrix; value decomposition; values
skew()
skew-symmetric matrix
span
sparse matrix
spectral radius
spectrum
square root of Hermitian matrix
stability matrix
stabilizability
stein matrix equation
stochastic matrix
submatrix
subspace
Sylvester matrix equation
Sylvester's law of inertia
symmetric matrix
symmetrizable matrix
symplectic matrix
T
Takagi decomposition
toeplitz matrix
|_ identities
trace
|_ derivative of; minimization of
transpose of a matrix
triangular matrix
tridiagonal matrix
U
unit-rank matrix
unitarily similar matrices
unitary
|_ equivalence; matrix
upper shift matrix
V
vandermonde matrix
vector
|_ Gaussian
| |_ complex; real
|_ norm
| |_ euclidean; p-norms
|_ product; space
vectorization
vectorized transpose