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