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