Chapter SLE: Systems of Linear Equations | |
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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 |