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Appendix SL Sage

SSLE Solving Systems of Linear Equations

Sage GS Getting Started

RREF Reduced Row-Echelon Form

Sage M Matrices
Sage V Vectors
Sage AM Augmented Matrix
Sage RO Row Operations
Sage RREF Reduced Row-Echelon Form

TSS Types of Solution Sets

Sage FDV Free and Dependent Variables
Sage RCLS Recognizing Consistency of a Linear System
Sage SS1 Solving Systems, Part 1

HSE Homogeneous Systems of Equations

Sage SHS Solving Homogeneous Systems
Sage NS Null Space
Sage SH Sage Help

NM Nonsingular Matrices

Sage NM Nonsingular Matrix
Sage IM Identity Matrix
Sage NME1 Nonsingular Matrix Equivalences, Round 1

VO Vector Operations

Sage VSCV Vector Spaces of Column Vectors
Sage VO Vector Operations
Sage ANC A Note on Coercion

LC Linear Combinations

Sage LC Linear Combinations
Sage SLC Solutions and Linear Combinations
Sage SS2 Solving Systems, Part 2
Sage PSHS Particular Solutions, Homogeneous Solutions

SS Spanning Sets

Sage SS Spanning Sets
Sage CSS Consistent Systems and Spans
Sage SSNS Spanning Sets for Null Spaces
Sage SS3 Solving Systems, Part 3

LI Linear Independence

Sage LI Linear Independence
Sage NME2 Nonsingular Matrix Equivalences, Round 2
Sage LISS Linearly Independent Spanning Sets

LDS Linear Dependence and Spans

Sage RLD Relations of Linear Dependence
Sage COV Casting Out Vectors
Sage RS Reducing a Span
Sage RES Reworking a Span

O Orthogonality

Sage EVIC Exact Versus Inexact Computations
Sage CNIP Conjugates, Norms and Inner Products
Sage OGS Orthogonality and Gram-Schmidt

MO Matrix Operations

Sage MS Matrix Spaces
Sage MO Matrix Operations

MM Matrix Multiplication

Sage MVP Matrix-Vector Product
Sage MM Matrix Multiplication
Sage PMM Properties of Matrix Multiplication

MISLE Matrix Inverses and Systems of Linear Equations

Sage MISLE Matrix Inverse, Systems of Equations

MINM Matrix Inverses and Nonsingular Matrices

Sage MI Matrix Inverse
Sage NME3 Nonsingular Matrix Equivalences, Round 3
Sage UM Unitary Matrices

CRS Column 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

FS Four Subsets

Sage LNS Left Null Spaces
Sage RRSM Row-Reducing a Symbolic Matrix
Sage EEF Extended Echelon Form

S Subspaces

Sage VS Vector Spaces

B Bases

Sage B Bases
Sage SUTH0 Sage Under The Hood, Round 0
Sage NME5 Nonsingular Matrix Equivalences, Round 5
Sage C Coordinates

D Dimension

Sage D Dimension
Sage RNM Rank and Nullity of a Matrix
Sage NME6 Nonsingular Matrix Equivalences, Round 6

PD Properties of Dimension

Sage DMS Dimensions of Matrix Subspaces

DM Determinant of a Matrix

Sage EM Elementary Matrices
Sage DM Determinant of a Matrix

PDM Properties of Determinants of Matrices

Sage NME7 Nonsingular Matrix Equivalences, Round 7
Sage PDM Properties of Determinants of Matrices

EE Eigenvalues and Eigenvectors

Sage EE Eigenvalues and Eigenvectors
Sage CEVAL Computing Eigenvalues
Sage CEVEC Computing Eigenvectors

PEE Properties of Eigenvalues and Eigenvectors

Sage NME8 Nonsingular Matrix Equivalences, Round 8

SD Similarity and Diagonalization

Sage SM Similar Matrices
Sage MD Matrix Diagonalization

LT Linear Transformations

Sage LTS Linear Transformations, Symbolic
Sage LTM Linear Transformations, Matrices
Sage LTB Linear Transformations, Bases
Sage PI Pre-Images
Sage OLT Operations on Linear Transformations

ILT Injective Linear Transformations

Sage ILT Injective Linear Transformations
Sage CILT Composition of Injective Linear Transformations

SLT Surjective Linear Transformations

Sage SLT Surjective Linear Transformations
Sage CSLT Composition of Surjective Linear Transformations

IVLT Invertible 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

VR Vector Representations

Sage VR Vector Representations
Sage SUTH2 Sage Under The Hood, Round 2

MR Matrix 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

CB Change 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