Index

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(i, j)-multiplier

(i, j)-pivot

(r — 1)-regular

B-basis

E_ij

I_n

J_{m, n}

LU-factorization

M-matrix

P-matrix

P_o-matrix

ΔTN

ΔTP

D_n

e

e_i

K-subdirect sum

Kth compound of A

m-by-n matrices over IF

m-by-n real matrices

n-by-n matrices over IF

tth Hadamard power

tth power of A

u-profile

adjacent edge condition

adjugate

allow

almost principal minor

almost totally positive matrix

alternating nodes

backward identity

basic oscillatory matrix

bidiagonal

elementary

factorization

generalized

matrix

biorthogonality

block

bounded ratio

Cauchy matrix

Cauchy-Binet identity

Cayley transform

checkerboard partial order

checkerboard sign pattern

chord

chordal graph

classical adjoint

clique

clique sum

collocation matrix

column compression of A

column space

complement

extended Perron

index set

Perron

Schur

completion

compound

compound kernel of order p

compression of A

conditions

(M)

adjacent edge

cycle

eigenvector determinant

set-theoretic zero

threshold

contiguous components

contiguous index set

contiguous minor

contiguous rank property

contiguous submatrix

control points

control polygon of the curve

convex hull of a submatrix

corner minor

determinant

diagonal

diagonal matrix

diagram

planar

weighted planar

dispersion

double echelon form

EB

EB matrix

eigenvector determinant conditions

elementary bidiagonal matrix

elimination

Neville

Whitney

essentially nonnegative matrix

eternally

eventually positive determinant

eventually TN

eventually TP

exponent

extended Perron complement at t

factorization

LU

bidiagonal

SEB

successive bidiagonal

Fischer matrices

Fischer’s inequality

gap

GEB

generalized corner minor

generalized EB matrix

generalized elementary bidiagonal ma trix

generator

graph

chordal

cycle

MLBC

Grassmannian

Green’s matrix

Hadamard core

Hadamard power

Hadamard product

Hadamard’s inequality

Hankel matrix

identity

Cauchy-Binet

Jacobi

Karlin

Plücker

short-term Plucker

Sylvester

identity matrix

IITN

IITN_k

index of an eigenvalue

index set

inequality

basic Koteljanskii

Fischer

Hadamard

Koteljanskii

Oppenheim

infinitesimal element

initial minor

initial sign of a vector

interlace

interval

InTN

InTN_k

IrTN

IrTN_k

Jacobi matrix

Jacobi’s identity

Jordan structure

Karlin’s identity

Koteljanskii matrix

Koteljanskii’s inequality

latitudinal section

leading principal submatrix

line

longitudinal section

lower triangular

majorization

majorizes

matrix

P

P_o

almost totally positive

basic oscillatory

bidiagonal

Cauchy

collocation

compressed

creation

derivation

diagonal

EB

elementary bidiagonal

essentially nonnegative

function

GEB

generalized bidiagonal

Green’s

Hankel

Hessenberg

identity

Jacobi

Koteljanskii

oscillatory

Pólya

partial

partial TN

partial TP

Pascal

polynomial

Routh-Hurwitz

signature

single pair

symmetric Pascal

Toeplitz

totally nonnegative

totally positive

triangular

triangular TN

triangular TP

tridiagonal

Vandermonde

matrix function

matrix of type D

matrix with entries a_ij

matrix-valued function

maximum sign variation of x

minimum sign variation of x

minor

almost principal

contiguous

corner

generalized corner

initial

principal

quasi-initial

quasi-principal

MLBC graph

monotone matrix

multiplier

network

planar

weighted planar

Neville elimination

node of a profile

nonzero Jordan structure

normal Jacobi matrix

normalized dominant

Oppenheim’s inequality

OSC

oscillatory

Pólya frequency function

Pólya frequency function of order k

Pólya frequency sequence

Pólya frequency sequence of order n

Pólya matrix

partial matrix

partial TN matrix

partial TP matrix

partitioned rank intersection property

Pascal matrix

Perron complement

Perron’s theorem

Perron-Frobenius theory

pivot

Plücker coordinate

Plücker relations

planar diagrams

planar networks

polynomial matrix

principal rank

principal rank property

principal submatrix

principle of biorthogonality

profile

qualitative Jordan structure

quasi-initial minor

quasi-principal minor

quasi-principal submatrix

rank

rank deficient

realizable

realization

requires

retractable set

retractions of a matrix

Routh-Hurwitz matrix

row space

Schur complement

SEB factorization

section rank property

sections

set of retractions

shadow

sign pattern

signature matrix

single pair matrix

spectral radius

spectral structure

spline of degree k with knots x_i

stable polynomial

stretch

subdiagonal

subdirect sum

submatrix

contiguous

leading

nonprincipal

principal

successive bidiagonal factorization

superdiagonal

swath

Sylvester’s identity

symmetric Pascal matrix

terminal sign of a vector

TN’

TN_k

TN’_k

Toeplitz matrix

total sign variation of x

totally nonnegative

matrix

totally nonzero

totally positive basis

function

matrix

sequence

system

TP_k

triangular

triangular TN

triangular TP

tridiagonal

tridiagonal matrix

unisigned

upper triangular

Vandermonde matrix

variation diminishing

weight of a collection

weight of a path

weighted planar diagram

Whitney elimination

Whitney’s Reduction result

zero lines