FCLA Notation

Appendix NL Notation

Symbol	Description	Location
$A$	Matrix	Definition M
${[A]}_{i j}$	Matrix Entries	Definition M
$v$	Column Vector	Definition CV
${[v]}_{i}$	Column Vector Entries	Definition CV
$0$	Zero Column Vector	Definition ZCV
$LS (A, b)$	Matrix Representation of a Linear System	Definition MRLS
$[A \| b]$	Augmented Matrix	Definition AM
$R_{i} \leftrightarrow R_{j}$	Row Operation, Swap	Definition RO
$α R_{i}$	Row Operation, Multiply	Definition RO
$α R_{i} + R_{j}$	Row Operation, Add	Definition RO
$r, D, F$	Reduced Row-Echelon Form Analysis	Definition RREF
$N (A)$	Null Space of a Matrix	Definition NSM
$I_{m}$	Identity Matrix	Definition IM
$C^{m}$	Vector Space of Column Vectors	Definition VSCV
$u = v$	Column Vector Equality	Definition CVE
$u + v$	Column Vector Addition	Definition CVA
$α u$	Column Vector Scalar Multiplication	Definition CVSM
$⟨ S ⟩$	Span of a Set of Vectors	Definition SSCV
$\overset{―}{u}$	Complex Conjugate of a Column Vector	Definition CCCV
$⟨ u, v ⟩$	Inner Product	Definition IP
$‖ v ‖$	Norm of a Vector	Definition NV
$e_{i}$	Standard Unit Vectors	Definition SUV
$M_{m n}$	Vector Space of Matrices	Definition VSM
$A = B$	Matrix Equality	Definition ME
$A + B$	Matrix Addition	Definition MA
$α A$	Matrix Scalar Multiplication	Definition MSM
$O$	Zero Matrix	Definition ZM
$A^{t}$	Transpose of a Matrix	Definition TM
$\overset{―}{A}$	Complex Conjugate of a Matrix	Definition CCM
$A^{*}$	Adjoint	Definition A
$A u$	Matrix-Vector Product	Definition MVP
$A B$	Matrix Multiplication	Definition MM
$A^{- 1}$	Matrix Inverse	Definition MI
$C (A)$	Column Space of a Matrix	Definition CSM
$R (A)$	Row Space of a Matrix	Definition RSM
$L (A)$	Left Null Space	Definition LNS
$U + V$	Sum of Subspaces	Definition SOS
$\dim (V)$	Dimension	Definition D
$n (A)$	Nullity of a Matrix	Definition NOM
$r (A)$	Rank of a Matrix	Definition ROM
$E_{i, j}$	Elementary Matrix, Swap	Definition ELEM
$E_{i} (α)$	Elementary Matrix, Multiply	Definition ELEM
$E_{i, j} (α)$	Elementary Matrix, Add	Definition ELEM
$A (i \| j)$	SubMatrix	Definition SM
$\| A \|$	Determinant of a Matrix, Bars	Definition DM
$det (A)$	Determinant of a Matrix, Functional	Definition DM
$α_{A} (λ)$	Algebraic Multiplicity of an Eigenvalue	Definition AME
$γ_{A} (λ)$	Geometric Multiplicity of an Eigenvalue	Definition GME
$T : U \to V$	Linear Transformation	Definition LT
$K (T)$	Kernel of a Linear Transformation	Definition KLT
$R (T)$	Range of a Linear Transformation	Definition RLT
$r (T)$	Rank of a Linear Transformation	Definition ROLT
$n (T)$	Nullity of a Linear Transformation	Definition NOLT
$ρ_{B} (w)$	Vector Representation	Definition VR
$M_{B, C}^{T}$	Matrix Representation	Definition MR
$α = β$	Complex Number Equality	Definition CNE
$α + β$	Complex Number Addition	Definition CNA
$α β$	Complex Number Multiplication	Definition CNM
$\overset{―}{α}$	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
$\| S \|$	Cardinality	Definition C
$S \cup T$	Set Union	Definition SU
$S \cap T$	Set Intersection	Definition SI
$\overset{―}{S}$	Set Complement	Definition SC

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