Notation

NM:normal인 M

pdM:positive-definite M(M(C)일 때랑, M(R)일 때 정의가 다름)

psdM:positive-semidefinite M(M(C)일 때랑, M(R)일 때 정의가 다름)

HM:Hermitian M

UM:Unitary M

LTM:lower triangular matrix

UTM:uppwer triangular matrix

conj(M):conjugate transpose of M

inv(M):inverse of M

M_(i,j):M의 (i,j) entry

symM:Symmetric matrix (Real Matrix만을 가리킴)

*Matrix의 property관련

Spec(M):M의 eigenvalues를 원소로하는 집합

SpecR(M):M의 Spectral Radius

rank(M):rank of M

det(M):determinant of M

egv(M):M의 eigenvalue

egv(M,egv):M의 eigenvalue의 eigenvector(normalized된 걸 가리킴)

egS(M,egv):M의 eigenvalue의 eigenspace

sgv(M):singular value of M

JCF(M):M의 Jordan Canonical Form

SMF(M):M의 Smith Canonical Form

CharPoly(M):M의 characteristic Polynomial

MinPoly(M):M의 minimal polynomial

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Topological Space

nbd(x):neighbourhood of x

open(x):open set containing x

nbd(E):neighbourhood of S

NTS:Normal Topological Space

Gd:G-delta set, i.e. countable intersection of open sets.

T2S:T2 space

R(sTS):The Field of Real numbers with the standard topology

LK:locally compact

KS:compact support

KC:compact closure

lptK:Limit point compact

seqK:sequentially compact

cl(E):closure of E

KGd:Compact and G-delta

LKT2S:Locally Compact T2 Space

cl(LKT2S):one-point compactification of LKT2S

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Topological Vector Space

bdd:bounded subset

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Normed Vector Space

|| ||:norm on nvs

nbdd:norm bounded subset