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
\(\elemswap{i}{j}\)	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
\(\algmult{A}{\lambda}\)	Algebraic Multiplicity of an Eigenvalue	Definition AME
\(\geomult{A}{\lambda}\)	Geometric Multiplicity of an Eigenvalue	Definition GME
\(\ltdefn{T}{U}{V}\)	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
\(\alpha=\beta\)	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

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