Notation

Notation

M A  Matrix
MC Aij  Matrix Components
CV v  Column Vector
CVC vi  Column Vector Components
ZCV 0  Zero Column Vector
MRLS SA,b  Matrix Representation of a Linear System
AM Ab  Augmented Matrix
RO Ri Rj, αRi, αRi + Rj  Row Operations
RREFA r, D, F  Reduced Row-Echelon Form Analysis
NSM NA  Null Space of a Matrix
IM Im  Identity Matrix
VSCV 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 S  Span of a Set of Vectors
CCCV u  Complex Conjugate of a Column Vector
IP u,v  Inner Product
NV v  Norm of a Vector
SUV ei  Standard Unit Vectors
VSM Mmn  Vector Space of Matrices
ME A = B  Matrix Equality
MA A + B  Matrix Addition
MSM αA  Matrix Scalar Multiplication
ZM O  Zero Matrix
TM At  Transpose of a Matrix
CCM A  Complex Conjugate of a Matrix
A A  Adjoint
MVP Au  Matrix-Vector Product
MI A1  Matrix Inverse
CSM CA  Column Space of a Matrix
RSM A  Row Space of a Matrix
LNS A  Left Null Space
D dim V   Dimension
NOM n A  Nullity of a Matrix
ROM r A  Rank of a Matrix
DS V = U W  Direct Sum
ELEM Ei,j, Ei α, Ei,j α  Elementary Matrix
SM A i|j  SubMatrix
DM A, det A  Determinant of a Matrix
AME αA λ  Algebraic Multiplicity of an Eigenvalue
GME γA λ  Geometric Multiplicity of an Eigenvalue
LT T : U V   Linear Transformation
KLT KT  Kernel of a Linear Transformation
RLT T  Range of a Linear Transformation
ROLT r T  Rank of a Linear Transformation
NOLT n T  Nullity of a Linear Transformation
VR ρB w  Vector Representation
MR MB,CT   Matrix Representation
JB Jn λ  Jordan Block
GES GT λ  Generalized Eigenspace
LTR T|U  Linear Transformation Restriction
IE ιT λ  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 S  Cardinality
SU S T  Set Union
SI S T  Set Intersection
SC S  Set Complement
T t A  Trace
HP A B  Hadamard Product
HID Jmn  Hadamard Identity
HI   Hadamard Inverse
SRM A12  Square Root of a Matrix