Section WILA: What is Linear Algebra?
Section SSLE: Solving Systems of Linear Equations
SLE System of Linear Equations
SSLE Solution of a System of Linear Equations
SSSLE Solution Set of a System of Linear Equations
ESYS Equivalent Systems
EO Equation Operations
Section RREF: Reduced Row-Echelon Form
M Matrix
CV Column Vector
ZCV Zero Column Vector
CM Coefficient Matrix
VOC Vector of Constants
SOLV Solution Vector
MRLS Matrix Representation of a Linear System
AM Augmented Matrix
RO Row Operations
REM Row-Equivalent Matrices
RREF Reduced Row-Echelon Form
Section TSS: Types of Solution Sets
CS Consistent System
IDV Independent and Dependent Variables
Section HSE: Homogeneous Systems of Equations
HS Homogeneous System
TSHSE Trivial Solution to Homogeneous Systems of Equations
NSM Null Space of a Matrix
Section NM: Nonsingular Matrices
SQM Square Matrix
NM Nonsingular Matrix
IM Identity Matrix
Section VO: Vector Operations
VSCV Vector Space of Column Vectors
CVE Column Vector Equality
CVA Column Vector Addition
CVSM Column Vector Scalar Multiplication
Section LC: Linear Combinations
LCCV Linear Combination of Column Vectors
Section SS: Spanning Sets
SSCV Span of a Set of Column Vectors
Section LI: Linear Independence
RLDCV Relation of Linear Dependence for Column Vectors
LICV Linear Independence of Column Vectors
Section LDS: Linear Dependence and Spans
Section O: Orthogonality
CCCV Complex Conjugate of a Column Vector
IP Inner Product
NV Norm of a Vector
OV Orthogonal Vectors
OSV Orthogonal Set of Vectors
SUV Standard Unit Vectors
ONS OrthoNormal Set
Section MO: Matrix Operations
VSM Vector Space of $m\times n$ Matrices
ME Matrix Equality
MA Matrix Addition
MSM Matrix Scalar Multiplication
ZM Zero Matrix
TM Transpose of a Matrix
SYM Symmetric Matrix
CCM Complex Conjugate of a Matrix
A Adjoint
Section MM: Matrix Multiplication
MVP Matrix-Vector Product
MM Matrix Multiplication
HM Hermitian Matrix
Section MISLE: Matrix Inverses and Systems of Linear Equations
MI Matrix Inverse
Section MINM: Matrix Inverses and Nonsingular Matrices
UM Unitary Matrices
Section CRS: Column and Row Spaces
CSM Column Space of a Matrix
RSM Row Space of a Matrix
Section FS: Four Subsets
LNS Left Null Space
EEF Extended Echelon Form
Section VS: Vector Spaces
VS Vector Space
Section S: Subspaces
S Subspace
TS Trivial Subspaces
LC Linear Combination
SS Span of a Set
Section LISS: Linear Independence and Spanning Sets
RLD Relation of Linear Dependence
LI Linear Independence
SSVS Spanning Set of a Vector Space
Section B: Bases
B Basis
Section D: Dimension
D Dimension
NOM Nullity Of a Matrix
ROM Rank Of a Matrix
Section PD: Properties of Dimension
Section DM: Determinant of a Matrix
ELEM Elementary Matrices
SM SubMatrix
DM Determinant of a Matrix
Section PDM: Properties of Determinants of Matrices
Section EE: Eigenvalues and Eigenvectors
EEM Eigenvalues and Eigenvectors of a Matrix
CP Characteristic Polynomial
EM Eigenspace of a Matrix
AME Algebraic Multiplicity of an Eigenvalue
GME Geometric Multiplicity of an Eigenvalue
Section PEE: Properties of Eigenvalues and Eigenvectors
Section SD: Similarity and Diagonalization
SIM Similar Matrices
DIM Diagonal Matrix
DZM Diagonalizable Matrix
Section LT: Linear Transformations
LT Linear Transformation
PI Pre-Image
LTA Linear Transformation Addition
LTSM Linear Transformation Scalar Multiplication
LTC Linear Transformation Composition
Section ILT: Injective Linear Transformations
ILT Injective Linear Transformation
KLT Kernel of a Linear Transformation
Section SLT: Surjective Linear Transformations
SLT Surjective Linear Transformation
RLT Range of a Linear Transformation
Section IVLT: Invertible Linear Transformations
IDLT Identity Linear Transformation
IVLT Invertible Linear Transformations
IVS Isomorphic Vector Spaces
ROLT Rank Of a Linear Transformation
NOLT Nullity Of a Linear Transformation
Section VR: Vector Representations
VR Vector Representation
Section MR: Matrix Representations
MR Matrix Representation
Section CB: Change of Basis
EELT Eigenvalue and Eigenvector of a Linear Transformation
CBM Change-of-Basis Matrix
Section OD: Orthonormal Diagonalization
UTM Upper Triangular Matrix
LTM Lower Triangular Matrix
NRML Normal Matrix
Section CNO: Complex Number Operations
CNE Complex Number Equality
CNA Complex Number Addition
CNM Complex Number Multiplication
CCN Conjugate of a Complex Number
MCN Modulus of a Complex Number
Section SET: Sets
SSET Subset
ES Empty Set
SE Set Equality
C Cardinality
SU Set Union
SI Set Intersection
SC Set Complement