Section WILA: What is Linear Algebra?
TMP Trail Mix Packaging
Section SSLE: Solving Systems of Linear Equations
STNE Solving two (nonlinear) equations
NSE Notation for a system of equations
TTS Three typical systems
US Three equations, one solution
IS Three equations, infinitely many solutions
Section RREF: Reduced Row-Echelon Form
AM A matrix
NSLE Notation for systems of linear equations
AMAA Augmented matrix for Archetype A
TREM Two row-equivalent matrices
USR Three equations, one solution, reprised
RREF A matrix in reduced row-echelon form
NRREF A matrix not in reduced row-echelon form
SAB Solutions for Archetype B
SAA Solutions for Archetype A
SAE Solutions for Archetype E
Section TSS: Types of Solution Sets
RREFN Reduced row-echelon form notation
ISSI Describing infinite solution sets, Archetype I
FDV Free and dependent variables
CFV Counting free variables
OSGMD One solution gives many, Archetype D
Section HSE: Homogeneous Systems of Equations
AHSAC Archetype C as a homogeneous system
HUSAB Homogeneous, unique solution, Archetype B
HISAA Homogeneous, infinite solutions, Archetype A
HISAD Homogeneous, infinite solutions, Archetype D
NSEAI Null space elements of Archetype I
CNS1 Computing a null space, no. 1
CNS2 Computing a null space, no. 2
Section NM: Nonsingular Matrices
S A singular matrix, Archetype A
NM A nonsingular matrix, Archetype B
IM An identity matrix
SRR Singular matrix, row-reduced
NSR Nonsingular matrix, row-reduced
NSS Null space of a singular matrix
NSNM Null space of a nonsingular matrix
Section VO: Vector Operations
VESE Vector equality for a system of equations
VA Addition of two vectors in $\complex{4}$
CVSM Scalar multiplication in $\complex{5}$
Section LC: Linear Combinations
TLC Two linear combinations in $\complex{6}$
ABLC Archetype B as a linear combination
AALC Archetype A as a linear combination
VFSAD Vector form of solutions for Archetype D
VFS Vector form of solutions
VFSAI Vector form of solutions for Archetype I
VFSAL Vector form of solutions for Archetype L
PSHS Particular solutions, homogeneous solutions, Archetype D
Section SS: Spanning Sets
ABS A basic span
SCAA Span of the columns of Archetype A
SCAB Span of the columns of Archetype B
SSNS Spanning set of a null space
NSDS Null space directly as a span
SCAD Span of the columns of Archetype D
Section LI: Linear Independence
LDS Linearly dependent set in $\complex{5}$
LIS Linearly independent set in $\complex{5}$
LIHS Linearly independent, homogeneous system
LDHS Linearly dependent, homogeneous system
LDRN Linearly dependent, $r$ and $n$
LLDS Large linearly dependent set in $\complex{4}$
LDCAA Linearly dependent columns in Archetype A
LICAB Linearly independent columns in Archetype B
LINSB Linear independence of null space basis
NSLIL Null space spanned by linearly independent set, Archetype L
Section LDS: Linear Dependence and Spans
RSC5 Reducing a span in $\complex{5}$
COV Casting out vectors
RSC4 Reducing a span in $\complex{4}$
RES Reworking elements of a span
Section O: Orthogonality
CSIP Computing some inner products
CNSV Computing the norm of some vectors
TOV Two orthogonal vectors
SUVOS Standard Unit Vectors are an Orthogonal Set
AOS An orthogonal set
GSTV Gram-Schmidt of three vectors
ONTV Orthonormal set, three vectors
ONFV Orthonormal set, four vectors
Section MO: Matrix Operations
MA Addition of two matrices in $M_{23}$
MSM Scalar multiplication in $M_{32}$
TM Transpose of a $3\times 4$ matrix
SYM A symmetric $5\times 5$ matrix
CCM Complex conjugate of a matrix
Section MM: Matrix Multiplication
MTV A matrix times a vector
MNSLE Matrix notation for systems of linear equations
MBC Money's best cities
PTM Product of two matrices
MMNC Matrix multiplication is not commutative
PTMEE Product of two matrices, entry-by-entry
Section MISLE: Matrix Inverses and Systems of Linear Equations
SABMI Solutions to Archetype B with a matrix inverse
MWIAA A matrix without an inverse, Archetype A
MI Matrix inverse
CMI Computing a matrix inverse
CMIAB Computing a matrix inverse, Archetype B
Section MINM: Matrix Inverses and Nonsingular Matrices
UM3 Unitary matrix of size 3
UPM Unitary permutation matrix
OSMC Orthonormal set from matrix columns
Section CRS: Column and Row Spaces
CSMCS Column space of a matrix and consistent systems
MCSM Membership in the column space of a matrix
CSTW Column space, two ways
CSOCD Column space, original columns, Archetype D
CSAA Column space of Archetype A
CSAB Column space of Archetype B
RSAI Row space of Archetype I
RSREM Row spaces of two row-equivalent matrices
IAS Improving a span
CSROI Column space from row operations, Archetype I
Section FS: Four Subsets
LNS Left null space
CSANS Column space as null space
SEEF Submatrices of extended echelon form
FS1 Four subsets, no. 1
FS2 Four subsets, no. 2
FSAG Four subsets, Archetype G
Section VS: Vector Spaces
VSCV The vector space $\complex{m}$
VSM The vector space of matrices, $M_{mn}$
VSP The vector space of polynomials, $P_n$
VSIS The vector space of infinite sequences
VSF The vector space of functions
VSS The singleton vector space
CVS The crazy vector space
PCVS Properties for the Crazy Vector Space
Section S: Subspaces
SC3 A subspace of $\complex{3}$
SP4 A subspace of $P_4$
NSC2Z A non-subspace in $\complex{2}$, zero vector
NSC2A A non-subspace in $\complex{2}$, additive closure
NSC2S A non-subspace in $\complex{2}$, scalar multiplication closure
RSNS Recasting a subspace as a null space
LCM A linear combination of matrices
SSP Span of a set of polynomials
SM32 A subspace of $M_{32}$
Section LISS: Linear Independence and Spanning Sets
LIP4 Linear independence in $P_4$
LIM32 Linear independence in $M_{32}$
LIC Linearly independent set in the crazy vector space
SSP4 Spanning set in $P_4$
SSM22 Spanning set in $M_{22}$
SSC Spanning set in the crazy vector space
AVR A vector representation
Section B: Bases
BP Bases for $P_n$
BM A basis for the vector space of matrices
BSP4 A basis for a subspace of $P_4$
BSM22 A basis for a subspace of $M_{22}$
BC Basis for the crazy vector space
RSB Row space basis
RS Reducing a span
CABAK Columns as Basis, Archetype K
CROB4 Coordinatization relative to an orthonormal basis, $\complex{4}$
CROB3 Coordinatization relative to an orthonormal basis, $\complex{3}$
Section D: Dimension
LDP4 Linearly dependent set in $P_4$
DSM22 Dimension of a subspace of $M_{22}$
DSP4 Dimension of a subspace of $P_4$
DC Dimension of the crazy vector space
VSPUD Vector space of polynomials with unbounded degree
RNM Rank and nullity of a matrix
RNSM Rank and nullity of a square matrix
Section PD: Properties of Dimension
BPR Bases for $P_n$, reprised
BDM22 Basis by dimension in $M_{22}$
SVP4 Sets of vectors in $P_4$
RRTI Rank, rank of transpose, Archetype I
Section DM: Determinant of a Matrix
EMRO Elementary matrices and row operations
SS Some submatrices
D33M Determinant of a $3\times 3$ matrix
TCSD Two computations, same determinant
DUTM Determinant of an upper triangular matrix
Section PDM: Properties of Determinants of Matrices
DRO Determinant by row operations
ZNDAB Zero and nonzero determinant, Archetypes A and B
Section EE: Eigenvalues and Eigenvectors
SEE Some eigenvalues and eigenvectors
PM Polynomial of a matrix
CAEHW Computing an eigenvalue the hard way
CPMS3 Characteristic polynomial of a matrix, size 3
EMS3 Eigenvalues of a matrix, size 3
ESMS3 Eigenspaces of a matrix, size 3
EMMS4 Eigenvalue multiplicities, matrix of size 4
ESMS4 Eigenvalues, symmetric matrix of size 4
HMEM5 High multiplicity eigenvalues, matrix of size 5
CEMS6 Complex eigenvalues, matrix of size 6
DEMS5 Distinct eigenvalues, matrix of size 5
Section PEE: Properties of Eigenvalues and Eigenvectors
BDE Building desired eigenvalues
Section SD: Similarity and Diagonalization
SMS5 Similar matrices of size 5
SMS3 Similar matrices of size 3
EENS Equal eigenvalues, not similar
DAB Diagonalization of Archetype B
DMS3 Diagonalizing a matrix of size 3
NDMS4 A non-diagonalizable matrix of size 4
DEHD Distinct eigenvalues, hence diagonalizable
HPDM High power of a diagonalizable matrix
FSCF Fibonacci sequence, closed form
Section LT: Linear Transformations
ALT A linear transformation
NLT Not a linear transformation
LTPM Linear transformation, polynomials to matrices
LTPP Linear transformation, polynomials to polynomials
LTM Linear transformation from a matrix
MFLT Matrix from a linear transformation
MOLT Matrix of a linear transformation
LTDB1 Linear transformation defined on a basis
LTDB2 Linear transformation defined on a basis
LTDB3 Linear transformation defined on a basis
SPIAS Sample pre-images, Archetype S
STLT Sum of two linear transformations
SMLT Scalar multiple of a linear transformation
CTLT Composition of two linear transformations
Section ILT: Injective Linear Transformations
NIAQ Not injective, Archetype Q
IAR Injective, Archetype R
IAV Injective, Archetype V
NKAO Nontrivial kernel, Archetype O
TKAP Trivial kernel, Archetype P
NIAQR Not injective, Archetype Q, revisited
NIAO Not injective, Archetype O
IAP Injective, Archetype P
NIDAU Not injective by dimension, Archetype U
Section SLT: Surjective Linear Transformations
NSAQ Not surjective, Archetype Q
SAR Surjective, Archetype R
SAV Surjective, Archetype V
RAO Range, Archetype O
FRAN Full range, Archetype N
NSAQR Not surjective, Archetype Q, revisited
NSAO Not surjective, Archetype O
SAN Surjective, Archetype N
BRLT A basis for the range of a linear transformation
NSDAT Not surjective by dimension, Archetype T
Section IVLT: Invertible Linear Transformations
AIVLT An invertible linear transformation
ANILT A non-invertible linear transformation
CIVLT Computing the Inverse of a Linear Transformations
IVSAV Isomorphic vector spaces, Archetype V
Section VR: Vector Representations
VRC4 Vector representation in $\complex{4}$
VRP2 Vector representations in $P_2$
TIVS Two isomorphic vector spaces
CVSR Crazy vector space revealed
ASC A subspace characterized
MIVS Multiple isomorphic vector spaces
CP2 Coordinatizing in $P_2$
CM32 Coordinatization in $M_{32}$
Section MR: Matrix Representations
OLTTR One linear transformation, three representations
ALTMM A linear transformation as matrix multiplication
MPMR Matrix product of matrix representations
KVMR Kernel via matrix representation
RVMR Range via matrix representation
ILTVR Inverse of a linear transformation via a representation
Section CB: Change of Basis
ELTBM Eigenvectors of linear transformation between matrices
ELTBP Eigenvectors of linear transformation between polynomials
CBP Change of basis with polynomials
CBCV Change of basis with column vectors
MRCM Matrix representations and change-of-basis matrices
MRBE Matrix representation with basis of eigenvectors
ELTT Eigenvectors of a linear transformation, twice
CELT Complex eigenvectors of a linear transformation
Section OD: Orthonormal Diagonalization
ANM A normal matrix
Section CNO: Complex Number Operations
ACN Arithmetic of complex numbers
CSCN Conjugate of some complex numbers
MSCN Modulus of some complex numbers
Section SET: Sets
SETM Set membership
SSET Subset
CS Cardinality and Size
SU Set union
SI Set intersection
SC Set complement