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\kern -1.95872pt \left (A,\kern 1.95872pt b\right ) Matrix
Representation of a Linear System
AM \left [\left .A\kern 1.95872pt \right \vert \kern 1.95872pt 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\kern -1.95872pt \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,\kern 1.95872pt 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\kern -1.95872pt \left (A\right ) Column
Space of a Matrix
RSM ℛ\kern -1.95872pt \left (A\right ) Row
Space of a Matrix
LNS ℒ\kern -1.95872pt \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 \left \vert A\right \vert ,
\mathop{ det} \left (A\right ) 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\kern -1.95872pt \left (T\right ) Kernel
of a Linear Transformation
RLT ℛ\kern -1.95872pt \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 α 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