## AppendixSLSage

##### SectionSSLESolving Systems of Linear Equations
Sage GS Getting Started
##### SectionRREFReduced Row-Echelon Form
Sage M Matrices
Sage V Vectors
Sage AM Augmented Matrix
Sage RO Row Operations
Sage RREF Reduced Row-Echelon Form
##### SectionTSSTypes of Solution Sets
Sage FDV Free and Dependent Variables
Sage RCLS Recognizing Consistency of a Linear System
Sage SS1 Solving Systems, Part 1
##### SectionHSEHomogeneous Systems of Equations
Sage SHS Solving Homogeneous Systems
Sage NS Null Space
Sage SH Sage Help
##### SectionNMNonsingular Matrices
Sage NM Nonsingular Matrix
Sage IM Identity Matrix
Sage NME1 Nonsingular Matrix Equivalences, Round 1
##### SectionVOVector Operations
Sage VSCV Vector Spaces of Column Vectors
Sage VO Vector Operations
Sage ANC A Note on Coercion
##### SectionLCLinear Combinations
Sage LC Linear Combinations
Sage SLC Solutions and Linear Combinations
Sage SS2 Solving Systems, Part 2
Sage PSHS Particular Solutions, Homogeneous Solutions
##### SectionSSSpanning Sets
Sage SS Spanning Sets
Sage CSS Consistent Systems and Spans
Sage SSNS Spanning Sets for Null Spaces
Sage SS3 Solving Systems, Part 3
##### SectionLILinear Independence
Sage LI Linear Independence
Sage NME2 Nonsingular Matrix Equivalences, Round 2
Sage LISS Linearly Independent Spanning Sets
##### SectionLDSLinear Dependence and Spans
Sage RLD Relations of Linear Dependence
Sage COV Casting Out Vectors
Sage RS Reducing a Span
Sage RES Reworking a Span
##### SectionOOrthogonality
Sage EVIC Exact Versus Inexact Computations
Sage CNIP Conjugates, Norms and Inner Products
Sage OGS Orthogonality and Gram-Schmidt
##### SectionMOMatrix Operations
Sage MS Matrix Spaces
Sage MO Matrix Operations
##### SectionMMMatrix Multiplication
Sage MVP Matrix-Vector Product
Sage MM Matrix Multiplication
Sage PMM Properties of Matrix Multiplication
##### SectionMISLEMatrix Inverses and Systems of Linear Equations
Sage MISLE Matrix Inverse, Systems of Equations
##### SectionMINMMatrix Inverses and Nonsingular Matrices
Sage MI Matrix Inverse
Sage NME3 Nonsingular Matrix Equivalences, Round 3
Sage UM Unitary Matrices
##### SectionCRSColumn and Row Spaces
Sage CSCS Column Space and Consistent Systems
Sage CSOC Column Space, Original Columns
Sage NME4 Nonsingular Matrix Equivalences, Round 4
Sage RSM Row Space of a Matrix
##### SectionFSFour Subsets
Sage LNS Left Null Spaces
Sage RRSM Row-Reducing a Symbolic Matrix
Sage EEF Extended Echelon Form
##### SectionSSubspaces
Sage VS Vector Spaces
##### SectionBBases
Sage B Bases
Sage SUTH0 Sage Under The Hood, Round 0
Sage NME5 Nonsingular Matrix Equivalences, Round 5
Sage C Coordinates
##### SectionDDimension
Sage D Dimension
Sage RNM Rank and Nullity of a Matrix
Sage NME6 Nonsingular Matrix Equivalences, Round 6
##### SectionPDProperties of Dimension
Sage DMS Dimensions of Matrix Subspaces
##### SectionDMDeterminant of a Matrix
Sage EM Elementary Matrices
Sage DM Determinant of a Matrix
##### SectionPDMProperties of Determinants of Matrices
Sage NME7 Nonsingular Matrix Equivalences, Round 7
Sage PDM Properties of Determinants of Matrices
##### SectionEEEigenvalues and Eigenvectors
Sage EE Eigenvalues and Eigenvectors
Sage CEVAL Computing Eigenvalues
Sage CEVEC Computing Eigenvectors
##### SectionPEEProperties of Eigenvalues and Eigenvectors
Sage NME8 Nonsingular Matrix Equivalences, Round 8
##### SectionSDSimilarity and Diagonalization
Sage SM Similar Matrices
Sage MD Matrix Diagonalization
##### SectionLTLinear Transformations
Sage LTS Linear Transformations, Symbolic
Sage LTM Linear Transformations, Matrices
Sage LTB Linear Transformations, Bases
Sage PI Preimages
Sage OLT Operations on Linear Transformations
##### SectionILTInjective Linear Transformations
Sage ILT Injective Linear Transformations
Sage CILT Composition of Injective Linear Transformations
##### SectionSLTSurjective Linear Transformations
Sage SLT Surjective Linear Transformations
Sage CSLT Composition of Surjective Linear Transformations
##### SectionIVLTInvertible Linear Transformations
Sage IVLT Invertible Linear Transformations
Sage CIVLT Computing the Inverse of a Linear Transformations
Sage LTOE Linear Transformation Odds and Ends
Sage SUTH1 Sage Under The Hood, Round 1
##### SectionVRVector Representations
Sage VR Vector Representations
Sage SUTH2 Sage Under The Hood, Round 2
##### SectionMRMatrix Representations
Sage MR Matrix Representations
Sage SUTH3 Sage Under The Hood, Round 3
Sage LTR Linear Transformation Restrictions
Sage NME9 Nonsingular Matrix Equivalences, Round 9
##### SectionCBChange of Basis
Sage ENDO Endomorphisms
Sage CBM Change-of-Basis Matrix
Sage MRCB Matrix Representation and Change-of-Basis
Sage CELT Designing Matrix Representations
Sage SUTH4 Sage Under The Hood, Round 4