Index Index
additive inverse
of a matrix, Definition
adjoint matrix, Definition
angle
between vectors, Definition
augmented matrix, Definition
cardinality
of a set, Definition
Cartesian product
arbitrary, Definition
finite, Definition
change of basis matrix, Definition
characteristic polynomial
of a matrix, Definition
column space
of a matrix, Definition
complex numbers, Definition
absolute value, Definition
addition, Definition
conjugation, Definition
imaginary part, Definition
modulus, Definition
multiplication, Definition
real part, Definition
consistent, Definition
determinant, Definition
diagonalizable, Definition
orthogonally, Definition
diagonalizing basis, Definition
dimension
of a vector space, Definition
distance
between two vectors, Definition
dot product, Definition
eigenbasis, Definition
eigenvalue, Definition
eigenvector, Definition
elementary matrix, Definition
elementary operations
linear systems, Definition
equation addition, Definition
equation swap, Definition
scalar multiplication, Definition
elementary row operations, Definition
row addition, Definition
row swap, Definition
scalar multiplication, Definition
Euclidean \(n\)-space, Definition
expansion along row/column, Definition
function, Definition
composition, Definition
equality, Definition
identity, Definition
image, Definition
image of a set, Definition
inverse, Definition
invertible, Definition
function space
\(C^n\), Definition
continuous, Definition
infinitely differentiable, Definition
polynomial, Definition
fundamental space
of a matrix, Definition
Gaussian elimination, Definition
Gram-Schmidt procedure, Procedure
identity matrix, Definition
image, Definition
inconsistent, Definition
injective
function, Definition
integers, Definition
invertible
function, Definition
linear transformation, Definition
matrix, Definition
isomorphism, Definition
linear combination
of matrices, Definition
of vectors, Definition
linear equation, Definition
linear independence, Definition
linear system, Definition
linear transformation
identity transformation, Definition
image, Definition
null space, Definition
zero transformation, Definition
mathematical induction, Subsection
strong induction, Subsubsection
weak induction, Subsubsection
matrices
diagonal, Definition
lower triangular, Definition
triangular, Definition
upper triangular, Definition
matrix, Definition
additive inverse, Definition
column vector, Definition
diagonal of square matrix, Definition
elementary, Definition
identity matrix, Definition
inverse, Definition
matrix entry notation, Item
matrix-building notation, Item
row vector, Definition
square, Definition
zero matrix, Definition
matrix addition, Definition
matrix multiplication, Definition
column method, Theorem
row method, Theorem
matrix polynomials, Definition
matrix powers, Definition
matrix scalar multiplication, Definition
matrix subtraction, Definition
matrix transformation, Definition
matrix transposition, Definition
minor of matrix, Definition
multiplicity of an eigenvalue
algebraic, Definition
geometric, Definition
norm
of a vector, Definition
null space
of a linear transformation, Definition
of a matrix, Definition Definition
nullity
of a linear transformation, Definition
of a matrix, Definition
one-to-one
function, Definition
one-to-one correspondence, Definition
onto
function, Definition
ordered basis, Definition
orthogonal
basis, Definition
complement (of a subspace), Definition
sets, Definition
vectors, Definition
orthogonally diagonalizable, Definition
orthonormal
basis, Definition Definition
parametric equations, Remark
polynomial, Definition
coefficient, Definition
constant term, Definition
degree, Definition Definition
expression, Definition
leading coefficient, Definition
leading term, Definition
rank
of a linear transformation, Definition
of a matrix, Definition
rank-nullity theorem, Theorem
rational numbers, Definition
real numbers, Definition
reflection
through a line, Definition
rotation
as linear transformation, Definition
row equivalence
of matrices, Definition
row reduction
of matrices, Definition
of systems, Definition
row space
of a matrix, Definition
sets, Definition
complement, Definition
difference, Definition
empty set, Definition
empty sets, Definition
equality, Definition
inclusion, Definition
intersection, Definition
membership, Definition
set builder notation, Definition
subset, Definition
union, Definition
similar matrices, Definition
skew-symmetric matrix, Definition
solutions to linear systems, Definition
span
of a set of vectors, Definition
spanning set, Definition
standard examples, Remark
submatrix, Definition
subspace, Definition
surjective
function, Definition
symmetric matrix, Definition
trace of a matrix, Definition
trace-zero matrix, Definition
transpose, Definition
tuple
arbitrary, Definition
finite, Definition
variables
free, Definition
leading, Definition
vector space, Definition
definition, Definition
of \(n\)-tuples, Definition
of infinite real sequences, Definition
of matrices, Definition
of positive real numbers, Definition
of real-valued functions on a set, Definition
subspace, Definition
vector, Definition
zero vector, Definition
zero vector space, Definition
Weighted Euclidean space, Definition
