FCLA Notation

Appendix NL Notation

Symbol	Description	Location
$A$	Matrix	Definition M
$\matrixentry{A}{ij}$	Matrix Entries	Definition M
$\vect{v}$	Column Vector	Definition CV
$\vectorentry{\vect{v}}{i}$	Column Vector Entries	Definition CV
$\zerovector$	Zero Column Vector	Definition ZCV
$\linearsystem{A}{\vect{b}}$	Matrix Representation of a Linear System	Definition MRLS
$\augmented{A}{\vect{b}}$	Augmented Matrix	Definition AM
$\rowopswap{i}{j}$	Row Operation, Swap	Definition RO
$\rowopmult{\alpha}{i}$	Row Operation, Multiply	Definition RO
$\rowopadd{\alpha}{i}{j}$	Row Operation, Add	Definition RO
$r,\ D,\ F$	Reduced Row-Echelon Form Analysis	Definition RREF
$\nsp{A}$	Null Space of a Matrix	Definition NSM
$I_m$	Identity Matrix	Definition IM
$\complex{m}$	Vector Space of Column Vectors	Definition VSCV
$\vect{u}=\vect{v}$	Column Vector Equality	Definition CVE
$\vect{u}+\vect{v}$	Column Vector Addition	Definition CVA
$\alpha\vect{u}$	Column Vector Scalar Multiplication	Definition CVSM
$\spn{S}$	Span of a Set of Vectors	Definition SSCV
$\conjugate{\vect{u}}$	Complex Conjugate of a Column Vector	Definition CCCV
$\innerproduct{\vect{u}}{\vect{v}}$	Inner Product	Definition IP
$\norm{\vect{v}}$	Norm of a Vector	Definition NV
$\vect{e}_i$	Standard Unit Vectors	Definition SUV
$M_{mn}$	Vector Space of Matrices	Definition VSM
$A=B$	Matrix Equality	Definition ME
$A+B$	Matrix Addition	Definition MA
$\alpha A$	Matrix Scalar Multiplication	Definition MSM
$\zeromatrix$	Zero Matrix	Definition ZM
$\transpose{A}$	Transpose of a Matrix	Definition TM
$\conjugate{A}$	Complex Conjugate of a Matrix	Definition CCM
$\adjoint{A}$	Adjoint	Definition A
$A\vect{u}$	Matrix-Vector Product	Definition MVP
$AB$	Matrix Multiplication	Definition MM
$\inverse{A}$	Matrix Inverse	Definition MI
$\csp{A}$	Column Space of a Matrix	Definition CSM
$\rsp{A}$	Row Space of a Matrix	Definition RSM
$\lns{A}$	Left Null Space	Definition LNS
$U+V$	Sum of Subspaces	Definition SOS
$\dimension{V}$	Dimension	Definition D
$\nullity{A}$	Nullity of a Matrix	Definition NOM
$\rank{A}$	Rank of a Matrix	Definition ROM
$\geomult{A}{\lambda}$	Geometric Multiplicity of an Eigenvalue	Definition GME
$\geneigenspace{A}{\lambda}$		Definition GES
$\algmult{A}{\lambda}$	Algebraic Multiplicity of an Eigenvalue	Definition AME
$\ltdefn{T}{U}{V}$	Linear Transformation	Definition LT
$\krn{T}$	Kernel of a Linear Transformation	Definition KLT
$\rng{T}$	Range of a Linear Transformation	Definition RLT
$\rank{T}$	Rank of a Linear Transformation	Definition ROLT
$\nullity{T}$	Nullity of a Linear Transformation	Definition NOLT
$\vectrep{B}{\vect{w}}$	Vector Representation	Definition VR
$\matrixrep{T}{B}{C}$	Matrix Representation	Definition MR
$\elemswap{i}{j}$	Elementary Matrix, Swap	Definition ELEM
$\elemmult{\alpha}{i}$	Elementary Matrix, Multiply	Definition ELEM
$\elemadd{\alpha}{i}{j}$	Elementary Matrix, Add	Definition ELEM
$\submatrix{A}{i}{j}$	SubMatrix	Definition SM
$\detbars{A}$	Determinant of a Matrix, Bars	Definition DM
$\detname{A}$	Determinant of a Matrix, Functional	Definition DM
$\alpha=\beta$	Complex Number Equality	Definition CNE
$\alpha+\beta$	Complex Number Addition	Definition CNA
$\alpha\beta$	Complex Number Multiplication	Definition CNM
$\conjugate{\alpha}$	Conjugate of a Complex Number	Definition CCN
$x\in S$	Set Membership	Definition SET
$S\subseteq T$	Subset	Definition SSET
$\emptyset$	Empty Set	Definition ES
$S=T$	Set Equality	Definition SE
$\card{S}$	Cardinality	Definition C
$S\cup T$	Set Union	Definition SU
$S\cap T$	Set Intersection	Definition SI
$\setcomplement{S}$	Set Complement	Definition SC