Chapter 2. 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 $\mathcal{ℒ}\mathcal{S}\left(A,b\right)$   Matrix Representation of a Linear System
AM $\left[\left.A\right|b\right]$   Augmented Matrix
RO $R_i\leftrightarrow R_j$ , $\alpha R_i$ , $\alpha R_i+R_j$   Row Operations
RREFA $r$ , $D$ , $F$   Reduced Row-Echelon Form Analysis
NSM $\mathcal{N}\left(A\right)$   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 $\alpha u$   Column Vector Scalar Multiplication
SSV $〈S〉$   Span of a Set of Vectors
CCCV $\stackrel{}{u}$   Complex Conjugate of a Column Vector
IP $〈u,v〉$   Inner Product
NV $‖v‖$   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 $\alpha A$   Matrix Scalar Multiplication
ZM $\mathcal{O}$   Zero Matrix
TM $A^t$   Transpose of a Matrix
CCM $\stackrel{}{A}$   Complex Conjugate of a Matrix
A $A^{\ast }$   Adjoint
MVP A $u$   Matrix-Vector Product
MI $A^{-1}$   Matrix Inverse
CSM $\mathcal{C}\left(A\right)$   Column Space of a Matrix
RSM $\mathcal{ℛ}\left(A\right)$   Row Space of a Matrix
LNS $\mathcal{ℒ}\left(A\right)$   Left Null Space
D $dim\left(V\right)$   Dimension
NOM $n\left(A\right)$   Nullity of a Matrix
ROM $r\left(A\right)$   Rank of a Matrix
DS $V=U\oplus W$   Direct Sum
ELEM $E_{i,j}$ , $E_i\left(\alpha \right)$ , $E_{i,j}\left(\alpha \right)$   Elementary Matrix
SM $A\left(i|j\right)$   SubMatrix
DM $\left|A\right|$ , $det\left(A\right)$   Determinant of a Matrix
AME ${\alpha }_A\left(\lambda \right)$   Algebraic Multiplicity of an Eigenvalue
GME ${\gamma }_A\left(\lambda \right)$   Geometric Multiplicity of an Eigenvalue
LT $T:U\to V$   Linear Transformation
KLT $\mathcal{K}\left(T\right)$   Kernel of a Linear Transformation
RLT $\mathcal{ℛ}\left(T\right)$   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 ${\rho }_B\left(w\right)$   Vector Representation
MR $M_{B,C}^T$   Matrix Representation
JB $J_n\left(\lambda \right)$   Jordan Block
GES ${\mathcal{G}}_T\left(\lambda \right)$   Generalized Eigenspace
LTR $T{|}_U$   Linear Transformation Restriction
IE ${\iota }_T\left(\lambda \right)$   Index of an Eigenvalue
CNE $\alpha =\beta$   Complex Number Equality
CNA $\alpha +\beta$   Complex Number Addition
CNM $\alpha \beta$   Complex Number Multiplication
CCN $\stackrel{}{\alpha }$   Conjugate of a Complex Number
SETM $x\in S$   Set Membership
SSET $S\subseteq T$   Subset
ES $\varnothing$   Empty Set
SE $S=T$   Set Equality
C $\left|S\right|$   Cardinality
SU $S\cup T$   Set Union
SI $S\cap T$   Set Intersection
SC $\stackrel{}{S}$   Set Complement
T $t\left(A\right)$   Trace
HP $A\circ B$   Hadamard Product
HID $J_{mn}$   Hadamard Identity
HI $\hat{A}$   Hadamard Inverse
SRM $A^{1∕2}$   Square Root of a Matrix