Section WILA: What is Linear Algebra? |
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 |