Definitions

Definitions

 
Section WILA
 
Section SSLE
Definition SLE System of Linear Equations
Definition ESYS Equivalent Systems
Definition EO Equation Operations
 
Section RREF
Definition M Matrix
Definition CV Column Vector
Definition ZCV Zero Column Vector
Definition CM Coefficient Matrix
Definition VOC Vector of Constants
Definition SV Solution Vector
Definition LSMR 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
Definition RR Row-Reducing
 
Section TSS
Definition CS Consistent System
Definition IDV Independent and Dependent Variables
 
Section HSE
Definition HS Homogeneous System
Definition TSHSE Trivial Solution to Homogeneous Systems of Equations
Definition NSM Null Space of a Matrix
 
Section NM
Definition SQM Square Matrix
Definition NM Nonsingular Matrix
Definition IM Identity Matrix
 
Section VO
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
Definition LCCV Linear Combination of Column Vectors
 
Section SS
Definition SSCV Span of a Set of Column Vectors
 
Section LI
Definition RLDCV Relation of Linear Dependence for Column Vectors
Definition LICV Linear Independence of Column Vectors
 
Section LDS
 
Section O
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 ONS OrthoNormal Set
 
Section MO
Definition VSM Vector Space of m × 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
Definition MVP Matrix-Vector Product
Definition MM Matrix Multiplication
Definition HM Hermitian Matrix
 
Section MISLE
Definition MI Matrix Inverse
Definition SUV Standard Unit Vectors
 
Section MINM
Definition UM Unitary Matrices
 
Section CRS
Definition CSM Column Space of a Matrix
Definition RSM Row Space of a Matrix
 
Section FS
Definition LNS Left Null Space
Definition EEF Extended Echelon Form
 
Section VS
Definition VS Vector Space
 
Section S
Definition S Subspace
Definition TS Trivial Subspaces
Definition LC Linear Combination
Definition SS Span of a Set
 
Section LISS
Definition RLD Relation of Linear Dependence
Definition LI Linear Independence
Definition TSVS To Span a Vector Space
 
Section B
Definition B Basis
 
Section D
Definition D Dimension
Definition NOM Nullity Of a Matrix
Definition ROM Rank Of a Matrix
 
Section PD
Definition DS Direct Sum
 
Section DM
Definition ELEM Elementary Matrices
Definition SM SubMatrix
Definition DM Determinant of a Matrix
 
Section PDM
 
Section EE
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 PEE
 
Section SD
Definition SIM Similar Matrices
Definition DIM Diagonal Matrix
Definition DZM Diagonalizable Matrix
 
Section LT
Definition LT Linear Transformation
Definition PI Pre-Image
Definition LTA Linear Transformation Addition
Definition LTSM Linear Transformation Scalar Multiplication
Definition LTC Linear Transformation Composition
 
Section ILT
Definition ILT Injective Linear Transformation
Definition KLT Kernel of a Linear Transformation
 
Section SLT
Definition SLT Surjective Linear Transformation
Definition RLT Range of a Linear Transformation
 
Section IVLT
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
Definition VR Vector Representation
 
Section MR
Definition MR Matrix Representation
 
Section CB
Definition EELT Eigenvalue and Eigenvector of a Linear Transformation
Definition CBM Change-of-Basis Matrix
 
Section OD
Definition UTM Upper Triangular Matrix
Definition LTM Lower Triangular Matrix
Definition NRML Normal Matrix
 
Section NLT
Definition NLT Nilpotent Linear Transformation
Definition JB Jordan Block
 
Section IS
Definition IS Invariant Subspace
Definition GEV Generalized Eigenvector
Definition GES Generalized Eigenspace
Definition LTR Linear Transformation Restriction
Definition IE Index of an Eigenvalue
 
Section JCF
Definition JCF Jordan Canonical Form
 
Section CNO
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
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
 
Section PT
 
Section F
Definition F Field
Definition IMP Integers Modulo a Prime
 
Section T
Definition T Trace
 
Section VM
Definition VM Vandermonde Matrix
 
Section PSM
Definition PSM Positive Semi-Definite Matrix
 
Section ROD
 
Section TD
 
Section SVD
Definition SV Singular Values
 
Section SR
Definition SRM Square Root of a Matrix
 
Section POD
 
Section CF
Definition LSS Least Squares Solution
 
Section SAS