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Appendix DL Definitions

SSLE Solving Systems of Linear Equations

Definition SLE System of Linear Equations
Definition SSLE Solution of a System of Linear Equations
Definition SSSLE Solution Set of a System of Linear Equations
Definition ESYS Equivalent Systems
Definition EO Equation Operations

RREF Reduced Row-Echelon Form

Definition M Matrix
Definition CV Column Vector
Definition ZCV Zero Column Vector
Definition CM Coefficient Matrix
Definition VOC Vector of Constants
Definition SOLV Solution Vector
Definition MRLS Matrix Representation of a Linear System
Definition AM Augmented Matrix
Definition RO Row Operations
Definition REM Row-Equivalent Matrices
Definition RREF Reduced Row-Echelon Form

TSS Types of Solution Sets

Definition CS Consistent System
Definition IDV Independent and Dependent Variables

HSE Homogeneous Systems of Equations

Definition HS Homogeneous System
Definition TSHSE Trivial Solution to Homogeneous Systems of Equations
Definition NSM Null Space of a Matrix

NM Nonsingular Matrices

Definition SQM Square Matrix
Definition NM Nonsingular Matrix
Definition IM Identity Matrix

VO Vector Operations

Definition VSCV Vector Space of Column Vectors
Definition CVE Column Vector Equality
Definition CVA Column Vector Addition
Definition CVSM Column Vector Scalar Multiplication

LC Linear Combinations

Definition LCCV Linear Combination of Column Vectors

SS Spanning Sets

Definition SSCV Span of a Set of Column Vectors

LI Linear Independence

Definition RLDCV Relation of Linear Dependence for Column Vectors
Definition LICV Linear Independence of Column Vectors

O Orthogonality

Definition CCCV Complex Conjugate of a Column Vector
Definition IP Inner Product
Definition NV Norm of a Vector
Definition OV Orthogonal Vectors
Definition OSV Orthogonal Set of Vectors
Definition SUV Standard Unit Vectors
Definition ONS OrthoNormal Set

MO Matrix Operations

Definition VSM Vector Space of \(m\times n\) Matrices
Definition ME Matrix Equality
Definition MA Matrix Addition
Definition MSM Matrix Scalar Multiplication
Definition ZM Zero Matrix
Definition TM Transpose of a Matrix
Definition SYM Symmetric Matrix
Definition CCM Complex Conjugate of a Matrix
Definition A Adjoint

MM Matrix Multiplication

Definition MVP Matrix-Vector Product
Definition MM Matrix Multiplication
Definition HM Hermitian Matrix

MISLE Matrix Inverses and Systems of Linear Equations

Definition MI Matrix Inverse

MINM Matrix Inverses and Nonsingular Matrices

Definition UM Unitary Matrices

CRS Column and Row Spaces

Definition CSM Column Space of a Matrix
Definition RSM Row Space of a Matrix

FS Four Subsets

Definition LNS Left Null Space
Definition EEF Extended Echelon Form

VS Vector Spaces

Definition VS Vector Space

S Subspaces

Definition S Subspace
Definition TS Trivial Subspaces
Definition LC Linear Combination
Definition SS Span of a Set

LISS Linear Independence and Spanning Sets

Definition RLD Relation of Linear Dependence
Definition LI Linear Independence
Definition SSVS Spanning Set of a Vector Space

B Bases

Definition B Basis

D Dimension

Definition D Dimension
Definition NOM Nullity Of a Matrix
Definition ROM Rank Of a Matrix

DM Determinant of a Matrix

Definition ELEM Elementary Matrices
Definition SM SubMatrix
Definition DM Determinant of a Matrix

EE Eigenvalues and Eigenvectors

Definition EEM Eigenvalues and Eigenvectors of a Matrix
Definition CP Characteristic Polynomial
Definition EM Eigenspace of a Matrix
Definition AME Algebraic Multiplicity of an Eigenvalue
Definition GME Geometric Multiplicity of an Eigenvalue

SD Similarity and Diagonalization

Definition SIM Similar Matrices
Definition DIM Diagonal Matrix
Definition DZM Diagonalizable Matrix

LT Linear Transformations

Definition LT Linear Transformation
Definition PI Pre-Image
Definition LTA Linear Transformation Addition
Definition LTSM Linear Transformation Scalar Multiplication
Definition LTC Linear Transformation Composition

ILT Injective Linear Transformations

Definition ILT Injective Linear Transformation
Definition KLT Kernel of a Linear Transformation

SLT Surjective Linear Transformations

Definition SLT Surjective Linear Transformation
Definition RLT Range of a Linear Transformation

IVLT Invertible Linear Transformations

Definition IDLT Identity Linear Transformation
Definition IVLT Invertible Linear Transformations
Definition IVS Isomorphic Vector Spaces
Definition ROLT Rank Of a Linear Transformation
Definition NOLT Nullity Of a Linear Transformation

VR Vector Representations

Definition VR Vector Representation

MR Matrix Representations

Definition MR Matrix Representation

CB Change of Basis

Definition EELT Eigenvalue and Eigenvector of a Linear Transformation
Definition CBM Change-of-Basis Matrix

OD Orthonormal Diagonalization

Definition UTM Upper Triangular Matrix
Definition LTM Lower Triangular Matrix
Definition NRML Normal Matrix

CNO Complex Number Operations

Definition CNE Complex Number Equality
Definition CNA Complex Number Addition
Definition CNM Complex Number Multiplication
Definition CCN Conjugate of a Complex Number
Definition MCN Modulus of a Complex Number

SET Sets

Definition SET Set
Definition SSET Subset
Definition ES Empty Set
Definition SE Set Equality
Definition C Cardinality
Definition SU Set Union
Definition SI Set Intersection
Definition SC Set Complement