## AppendixNLNotation

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
$$\dimension{V}$$ 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