Notation

Notation

M A  Matrix
MC {\left [A\right ]}_{ij}  Matrix Components
CV v  Column Vector
CVC {\left [v\right ]}_{i}  Column Vector Components
ZCV 0  Zero Column Vector
MRLS ℒS\left (A, b\right )  Matrix Representation of a Linear System
AM \left [\left .A\right \vert b\right ]  Augmented Matrix
RO {R}_{i} ↔ {R}_{j}, α{R}_{i}, α{R}_{i} + {R}_{j}  Row Operations
RREFA r, D, F  Reduced Row-Echelon Form Analysis
NSM N\left (A\right )  Null Space of a Matrix
IM {I}_{m}  Identity Matrix
VSCV {ℂ}^{m}  Vector Space of Column Vectors
CVE u = v  Column Vector Equality
CVA u + v  Column Vector Addition
CVSM αu  Column Vector Scalar Multiplication
SSV \left \langle S\right \rangle   Span of a Set of Vectors
CCCV u  Complex Conjugate of a Column Vector
IP \left \langle u, v\right \rangle   Inner Product
NV \left \Vert v\right \Vert   Norm of a Vector
SUV {e}_{i}  Standard Unit Vectors
VSM {M}_{mn}  Vector Space of Matrices
ME A = B  Matrix Equality
MA A + B  Matrix Addition
MSM αA  Matrix Scalar Multiplication
ZM O  Zero Matrix
TM {A}^{t}  Transpose of a Matrix
CCM A  Complex Conjugate of a Matrix
A {A}^{∗}  Adjoint
MVP Au  Matrix-Vector Product
MI {A}^{−1}  Matrix Inverse
CSM C\left (A\right )  Column Space of a Matrix
RSM ℛ\left (A\right )  Row Space of a Matrix
LNS ℒ\left (A\right )  Left Null Space
D \mathop{ dim}\nolimits \left (V \right )  Dimension
NOM n\left (A\right )  Nullity of a Matrix
ROM r\left (A\right )  Rank of a Matrix
DS V = U ⊕ W  Direct Sum
ELEM {E}_{i,j}, {E}_{i}\left (α\right ), {E}_{i,j}\left (α\right )  Elementary Matrix
SM A\left (i|j\right )  SubMatrix
DM \mathop{ det} \left (A\right ), \left \vert A\right \vert   Determinant of a Matrix
AME {α}_{A}\left (λ\right )  Algebraic Multiplicity of an Eigenvalue
GME {γ}_{A}\left (λ\right )  Geometric Multiplicity of an Eigenvalue
LT T : U↦V   Linear Transformation
KLT K\left (T\right )  Kernel of a Linear Transformation
RLT ℛ\left (T\right )  Range of a Linear Transformation
ROLT r\left (T\right )  Rank of a Linear Transformation
NOLT n\left (T\right )  Nullity of a Linear Transformation
VR {ρ}_{B}\left (w\right )  Vector Representation
MR {M}_{B,C}^{T }  Matrix Representation
JB {J}_{n}\left (λ\right )  Jordan Block
GES {G}_{T }\left (λ\right )  Generalized Eigenspace
LTR T{|}_{U}  Linear Transformation Restriction
IE {ι}_{T }\left (λ\right )  Index of an Eigenvalue
CNE α = β  Complex Number Equality
CNA α + β  Complex Number Addition
CNM αβ  Complex Number Multiplication
CCN c  Conjugate of a Complex Number
SETM x ∈ S  Set Membership
SSET S ⊆ T  Subset
ES   Empty Set
SE S = T  Set Equality
C \left \vert S\right \vert   Cardinality
SU S ∪ T  Set Union
SI S ∩ T  Set Intersection
SC S  Set Complement
T t\left (A\right )  Trace
HP A ∘ B  Hadamard Product
HID {J}_{mn}  Hadamard Identity
HI \widehat{A}  Hadamard Inverse
SRM {A}^{1∕2}  Square Root of a Matrix