Section WILA: What is Linear Algebra? | |
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Section SSLE: Solving Systems of Linear Equations | |

SLE | System of Linear Equations |

SSLE | Solution of a System of Linear Equations |

SSSLE | Solution Set of a System of Linear Equations |

ESYS | Equivalent Systems |

EO | Equation Operations |

Section RREF: Reduced Row-Echelon Form | |

M | Matrix |

CV | Column Vector |

ZCV | Zero Column Vector |

CM | Coefficient Matrix |

VOC | Vector of Constants |

SOLV | Solution Vector |

MRLS | Matrix Representation of a Linear System |

AM | Augmented Matrix |

RO | Row Operations |

REM | Row-Equivalent Matrices |

RREF | Reduced Row-Echelon Form |

Section TSS: Types of Solution Sets | |

CS | Consistent System |

IDV | Independent and Dependent Variables |

Section HSE: Homogeneous Systems of Equations | |

HS | Homogeneous System |

TSHSE | Trivial Solution to Homogeneous Systems of Equations |

NSM | Null Space of a Matrix |

Section NM: Nonsingular Matrices | |

SQM | Square Matrix |

NM | Nonsingular Matrix |

IM | Identity Matrix |

Section VO: Vector Operations | |

VSCV | Vector Space of Column Vectors |

CVE | Column Vector Equality |

CVA | Column Vector Addition |

CVSM | Column Vector Scalar Multiplication |

Section LC: Linear Combinations | |

LCCV | Linear Combination of Column Vectors |

Section SS: Spanning Sets | |

SSCV | Span of a Set of Column Vectors |

Section LI: Linear Independence | |

RLDCV | Relation of Linear Dependence for Column Vectors |

LICV | Linear Independence of Column Vectors |

Section LDS: Linear Dependence and Spans | |

Section O: Orthogonality | |

CCCV | Complex Conjugate of a Column Vector |

IP | Inner Product |

NV | Norm of a Vector |

OV | Orthogonal Vectors |

OSV | Orthogonal Set of Vectors |

SUV | Standard Unit Vectors |

ONS | OrthoNormal Set |

Section MO: Matrix Operations | |

VSM | Vector Space of $m\times n$ Matrices |

ME | Matrix Equality |

MA | Matrix Addition |

MSM | Matrix Scalar Multiplication |

ZM | Zero Matrix |

TM | Transpose of a Matrix |

SYM | Symmetric Matrix |

CCM | Complex Conjugate of a Matrix |

A | Adjoint |

Section MM: Matrix Multiplication | |

MVP | Matrix-Vector Product |

MM | Matrix Multiplication |

HM | Hermitian Matrix |

Section MISLE: Matrix Inverses and Systems of Linear Equations | |

MI | Matrix Inverse |

Section MINM: Matrix Inverses and Nonsingular Matrices | |

UM | Unitary Matrices |

Section CRS: Column and Row Spaces | |

CSM | Column Space of a Matrix |

RSM | Row Space of a Matrix |

Section FS: Four Subsets | |

LNS | Left Null Space |

EEF | Extended Echelon Form |

Section VS: Vector Spaces | |

VS | Vector Space |

Section S: Subspaces | |

S | Subspace |

TS | Trivial Subspaces |

LC | Linear Combination |

SS | Span of a Set |

Section LISS: Linear Independence and Spanning Sets | |

RLD | Relation of Linear Dependence |

LI | Linear Independence |

SSVS | Spanning Set of a Vector Space |

Section B: Bases | |

B | Basis |

Section D: Dimension | |

D | Dimension |

NOM | Nullity Of a Matrix |

ROM | Rank Of a Matrix |

Section PD: Properties of Dimension | |

Section DM: Determinant of a Matrix | |

ELEM | Elementary Matrices |

SM | SubMatrix |

DM | Determinant of a Matrix |

Section PDM: Properties of Determinants of Matrices | |

Section EE: Eigenvalues and Eigenvectors | |

EEM | Eigenvalues and Eigenvectors of a Matrix |

CP | Characteristic Polynomial |

EM | Eigenspace of a Matrix |

AME | Algebraic Multiplicity of an Eigenvalue |

GME | Geometric Multiplicity of an Eigenvalue |

Section PEE: Properties of Eigenvalues and Eigenvectors | |

Section SD: Similarity and Diagonalization | |

SIM | Similar Matrices |

DIM | Diagonal Matrix |

DZM | Diagonalizable Matrix |

Section LT: Linear Transformations | |

LT | Linear Transformation |

PI | Pre-Image |

LTA | Linear Transformation Addition |

LTSM | Linear Transformation Scalar Multiplication |

LTC | Linear Transformation Composition |

Section ILT: Injective Linear Transformations | |

ILT | Injective Linear Transformation |

KLT | Kernel of a Linear Transformation |

Section SLT: Surjective Linear Transformations | |

SLT | Surjective Linear Transformation |

RLT | Range of a Linear Transformation |

Section IVLT: Invertible Linear Transformations | |

IDLT | Identity Linear Transformation |

IVLT | Invertible Linear Transformations |

IVS | Isomorphic Vector Spaces |

ROLT | Rank Of a Linear Transformation |

NOLT | Nullity Of a Linear Transformation |

Section VR: Vector Representations | |

VR | Vector Representation |

Section MR: Matrix Representations | |

MR | Matrix Representation |

Section CB: Change of Basis | |

EELT | Eigenvalue and Eigenvector of a Linear Transformation |

CBM | Change-of-Basis Matrix |

Section OD: Orthonormal Diagonalization | |

UTM | Upper Triangular Matrix |

LTM | Lower Triangular Matrix |

NRML | Normal Matrix |

Section CNO: Complex Number Operations | |

CNE | Complex Number Equality |

CNA | Complex Number Addition |

CNM | Complex Number Multiplication |

CCN | Conjugate of a Complex Number |

MCN | Modulus of a Complex Number |

Section SET: Sets | |

SET | Set |

SSET | Subset |

ES | Empty Set |

SE | Set Equality |

C | Cardinality |

SU | Set Union |

SI | Set Intersection |

SC | Set Complement |