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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