FCLA Sage

Appendix SL Sage

Section SSLE Solving Systems of Linear Equations

Sage GS Getting Started

Section 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

Section 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

Section HSE Homogeneous Systems of Equations

Sage SHS Solving Homogeneous Systems

Sage NS Null Space

Sage SH Sage Help

Section NM Nonsingular Matrices

Sage NM Nonsingular Matrix

Sage IM Identity Matrix

Sage NME1 Nonsingular Matrix Equivalences, Round 1

Section VO Vector Operations

Sage VSCV Vector Spaces of Column Vectors

Sage VO Vector Operations

Sage ANC A Note on Coercion

Section 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

Section 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

Section LI Linear Independence

Sage LI Linear Independence

Sage NME2 Nonsingular Matrix Equivalences, Round 2

Sage LISS Linearly Independent Spanning Sets

Section 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

Section O Orthogonality

Sage EVIC Exact Versus Inexact Computations

Sage CNIP Conjugates, Norms and Inner Products

Sage OGS Orthogonality and Gram-Schmidt

Section MO Matrix Operations

Sage MS Matrix Spaces

Sage MO Matrix Operations

Section MM Matrix Multiplication

Sage MVP Matrix-Vector Product

Sage MM Matrix Multiplication

Sage PMM Properties of Matrix Multiplication

Section MISLE Matrix Inverses and Systems of Linear Equations

Sage MISLE Matrix Inverse, Systems of Equations

Section MINM Matrix Inverses and Nonsingular Matrices

Sage MI Matrix Inverse

Sage NME3 Nonsingular Matrix Equivalences, Round 3

Sage UM Unitary Matrices

Section 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

Section FS Four Subsets

Sage LNS Left Null Spaces

Sage RRSM Row-Reducing a Symbolic Matrix

Sage EEF Extended Echelon Form

Section S Subspaces

Sage VS Vector Spaces

Section B Bases

Sage B Bases

Sage SUTH0 Sage Under The Hood, Round 0

Sage NME5 Nonsingular Matrix Equivalences, Round 5

Sage C Coordinates

Section D Dimension

Sage D Dimension

Sage RNM Rank and Nullity of a Matrix

Sage NME6 Nonsingular Matrix Equivalences, Round 6

Section PD Properties of Dimension

Sage DMS Dimensions of Matrix Subspaces

Section DM Determinant of a Matrix

Sage EM Elementary Matrices

Sage DM Determinant of a Matrix

Section PDM Properties of Determinants of Matrices

Sage NME7 Nonsingular Matrix Equivalences, Round 7

Sage PDM Properties of Determinants of Matrices

Section EE Eigenvalues and Eigenvectors

Sage EE Eigenvalues and Eigenvectors

Sage CEVAL Computing Eigenvalues

Sage CEVEC Computing Eigenvectors

Section PEE Properties of Eigenvalues and Eigenvectors

Sage NME8 Nonsingular Matrix Equivalences, Round 8

Section SD Similarity and Diagonalization

Sage SM Similar Matrices

Sage MD Matrix Diagonalization

Section LT Linear 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

Section ILT Injective Linear Transformations

Sage ILT Injective Linear Transformations

Sage CILT Composition of Injective Linear Transformations

Section SLT Surjective Linear Transformations

Sage SLT Surjective Linear Transformations

Sage CSLT Composition of Surjective Linear Transformations

Section 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

Section VR Vector Representations

Sage VR Vector Representations

Sage SUTH2 Sage Under The Hood, Round 2

Section 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

Section 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