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Appendix DL Definitions

Section 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
Section 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
Section TSS Types of Solution Sets
Definition CS Consistent System
Definition IDV Independent and Dependent Variables
Section 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
Section NM Nonsingular Matrices
Definition SQM Square Matrix
Definition NM Nonsingular Matrix
Definition IM Identity Matrix
Section 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
Section LC Linear Combinations
Definition LCCV Linear Combination of Column Vectors
Section SS Spanning Sets
Definition SSCV Span of a Set of Column Vectors
Section LI Linear Independence
Definition RLDCV Relation of Linear Dependence for Column Vectors
Definition LICV Linear Independence of Column Vectors
Section 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
Section 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
Section MM Matrix Multiplication
Definition MVP Matrix-Vector Product
Definition MM Matrix Multiplication
Definition HM Hermitian Matrix
Section MISLE Matrix Inverses and Systems of Linear Equations
Definition MI Matrix Inverse
Section MINM Matrix Inverses and Nonsingular Matrices
Definition UM Unitary Matrices
Section CRS Column and Row Spaces
Definition CSM Column Space of a Matrix
Definition RSM Row Space of a Matrix
Section FS Four Subsets
Definition LNS Left Null Space
Definition EEF Extended Echelon Form
Section VS Vector Spaces
Definition VS Vector Space
Section S Subspaces
Definition S Subspace
Definition TS Trivial Subspaces
Definition LC Linear Combination
Definition SS Span of a Set
Definition SOS Sum of Subspaces
Section LISS Linear Independence and Spanning Sets
Definition RLD Relation of Linear Dependence
Definition LI Linear Independence
Definition SSVS Spanning Set of a Vector Space
Section B Bases
Definition B Basis
Section D Dimension
Definition D Dimension
Definition NOM Nullity Of a Matrix
Definition ROM Rank Of a Matrix
Section DM Determinant of a Matrix
Definition ELEM Elementary Matrices
Definition SM SubMatrix
Definition DM Determinant of a Matrix
Section 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
Section SD Similarity and Diagonalization
Definition SIM Similar Matrices
Definition DIM Diagonal Matrix
Definition DZM Diagonalizable Matrix
Section LT Linear Transformations
Definition LT Linear Transformation
Definition PI Preimage
Definition LTA Linear Transformation Addition
Definition LTSM Linear Transformation Scalar Multiplication
Definition LTC Linear Transformation Composition
Section ILT Injective Linear Transformations
Definition ILT Injective Linear Transformation
Definition KLT Kernel of a Linear Transformation
Section SLT Surjective Linear Transformations
Definition SLT Surjective Linear Transformation
Definition RLT Range of a Linear Transformation
Section 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
Section VR Vector Representations
Definition VR Vector Representation
Section MR Matrix Representations
Definition MR Matrix Representation
Section CB Change of Basis
Definition EELT Eigenvalue and Eigenvector of a Linear Transformation
Definition CBM Change-of-Basis Matrix
Section OD Orthonormal Diagonalization
Definition UTM Upper Triangular Matrix
Definition LTM Lower Triangular Matrix
Definition NRML Normal Matrix
Section 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
Section 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