Index Index
\(LU\) factorization, Paragraph
back substitution, Paragraph
back-face culling, Subsection
basic variable, Definition
basis, Definition
basis for a vector space, Definition
Binet's formula, Paragraph
Cauchy-Schwarz inequality
in \(\R^n\), Exercise
in \(\R^n\) with respect to an inner product, Exercise
Cayley-Hamilton Theorem, Corollary
change of basis matrix in \(\R^n\), Subsection Definition
characteristic equation, Definition
characteristic polynomial, Definition
characteristic value, Definition
characteristic vector, Definition
circuits
junctions, Paragraph
resistor, Paragraph
source, Paragraph
codomain of a matrix transformation, Subsection
coefficient matrix, Paragraph
cofactor, Subsection
column space, Definition
companion matrix, Exercise
complex conjugate, Paragraph
complex number, Definition
imaginary part, Paragraph
real part, Paragraph
condition number of a matrix, Definition
contraction, Project Activity
coordinate transformation, Subsection Definition
coordinate vector with respect to a basis, Definition
coordinate vector with respect to a basis in \(\R^n\), Definition
coordinates with respect to a basis, Definition
coordinates with respect to a basis in \(\R^n\), Definition
covariance matrix, Project Activity
Cramer's Rule, Theorem
cross product, Project Activity
defective matrix, Paragraph
dependence
linear, Definition
determinant, Definition
diagonal matrix, Item
diagonal of a matrix, Paragraph
differential equation, Paragraph
dimension
subspace of \(\R^n\), Definition
direct sum of subspaces, Definition
distance between vectors, Definition
distance between vectors in an inner product space, Definition
domain of a matrix transformation, Subsection
dominant eigenvalue, Paragraph
dominant eigenvector, Paragraph
dot product, Paragraph Definition
dynamical system, Subsection
eigenspace, Definition
eigenvalue, Definition
eigenvector, Definition
generalized, Definition
elementary operations, Subsection
equivalent statements, Paragraph
Fibonacci sequence, Subsection
field, Paragraph
forward elimination, Paragraph
Fourier coefficients, Project Activity
free variable, Definition
Gaussian quadrature, Subsection
Gershgorin Disk Theorem, Activity
Gram-Schmidt Process
in \(\R^n\), Theorem
in an inner product space, Theorem
identity matrix, Definition
image of a linear transformation, Paragraph
image of a matrix transformation, Paragraph
image of an element under a transformation, Subsection Paragraph
independence
linear, Definition
index, Paragraph
inner product, Definition Definition
inner product space, Definition
input-output models, Subsection
invariant subspace, Definition
Invertible Matrix Theorem, Theorem
isometry, Paragraph
isomorphism, Definition
iterated function system, Paragraph
Lagrange polynomials, Paragraph
Latent Semantic Indexing, Subsection
leading entry of a row, Paragraph
length of a vector in an inner product space, Definition
Leslie matrix, Paragraph
linear combination, Definition
weights, Definition
linear combination of vectors in a vector space, Definition
linear dependence, Definition
linear dependent vectors in a vector space, Definition
linear equation, Definition
coefficients, Definition
linear independence, Definition
linear transformation, Definition
diagonalizable, Definition
eigenvalue, Definition
eigenvector, Definition
kernel, Definition
matrix of, Definition
onto, Definition Definition
standard matrix, Definition
linearly independent vectors in a vector space, Definition
lower triangular matrix, Item
Markov process, Example Definition
matrix, Definition
adjugate, Activity
column, Paragraphs
columns, Paragraph
diagonalizable, Definition
elementary, Definition
entry, Paragraphs
exponential, Exercise
indefinite, Definition
inverse, Definition
invertible, Definition
minor, Subsection
negative definite, Definition
negative semidefinite, Definition
nilpotent, Example
non-singular, Paragraph
orthogonal, Definition
positive definite, Definition
positive semidefinite, Definition
product, Definition
row, Paragraphs
rows, Paragraph
scalar multiple, Paragraph
singular, Paragraph
size, Paragraphs Paragraph
sparse, Paragraph
square, Paragraph
sum, Paragraph
transpose, Definition
matrix transformation, Definition
matrix-vector product, Definition
moment of inertia, Subsection
multiplicity
algebraic, Definition
geometric, Definition
nilpotent matrix, Definition
nilpotent transfomation, Definition
nonhomogeneous system, Preview Activity
normal vector, Paragraph
null space, Definition
nullity of a matrix, Paragraph
Ohm's Law, Subsection
one-to-one, Definition
onto, Definition
operator norm of a matrix, Definition
orthogonal, Definition
orthogonal basis in \(\R^n\), Definition
orthogonal basis in an inner product space, Definition
orthogonal complement, Definition
orthogonal complement in inner product spaces, Definition
orthogonal diagonalization, Definition
orthogonal projection
in the direction of a vector, Definition
orthogonal projection onto a subspace, Definition
orthogonal set in \(\R^n\), Definition
orthogonal set in an inner product space, Definition
orthogonal vectors in inner product spaces, Definition
orthonormal basis in \(\R^n\), Definition
orthonormal basis in an inner product space, Definition
outer product decomposition, Paragraph
parametric vector form, Preview Activity
partitioned matrices, Paragraph
pivot, Definition Definition
pivot column, Paragraph
pivot positions, Paragraph
polynomial curve fitting, Paragraph
power method, Paragraph
projection
orthogonal to a vector, Definition
projection matrix, Definition
projection onto a subspace
in \(\R^n\), Definition
projection orthogonal to a subspace, Definition Definition
pseudoinverse, Paragraph
Pythagorean Theorem in \(\R^n\), Exercise
Pythagorean Theorem in \(\R^n\) with respect to an inner product, Exercise
quadratic form, Definition
range of a linear transformation, Definition
range of a matrix transformation, Subsection Definition
rank of a matrix, Paragraph
Rayleigh quotients, Paragraph
rotation matrix, Project Activity
rotation-scaling matrices, Paragraph
row echelon form, Definition
reduced, Definition
row equivalent matrices, Definition
row operations, Paragraph
row space, Definition
scalar product, Definition
scalars, Paragraph Paragraphs
self-similar set, Paragraph
shear, Project Activity Definition
similar matrices, Definition
singular values, Definition
singular vectors
left, Paragraphs
right, Paragraphs
span, Definition
span of a set of vectors in a vector space, Definition
spanning set, Paragraph
spectral decomposition, Paragraph
spectrum of a matrix, Paragraph
standard basis
for \(\pol_n\), Activity
for \(\R^n\), Paragraph
state vector, Paragraph
stochastic matrix, Definition
regular, Definition
Strassen's algorithm, Subsection
strictly diagonally dominant matrix, Definition
subspace
of \(\R^n\), Definition
subspace of a vector space, Definition
subspace of a vector space spanned by a set of vectors, Paragraph
symmetric matrix, Item
system of linear equations, Definition
consistent, Paragraphs
elimination, Paragraph
equivalent systems, Subsection
inconsistent, Paragraphs
operations, Subsection
solution, Definition
solution set, Paragraph
trace, Definition
transformation
matrix, Definition
triangle inequality in \(\R^n\), Exercise
triangle inequality in \(\R^n\) with respect to an inner product, Exercise
trigonometric polynomial, Paragraph
unit vector, Definition
unit vector in an inner product space, Definition
upper triangular matrix, Item
vector, Definition
column, Paragraph
component, Definition
entry, Definition
magnitude in \(\R^n\), Paragraph
norm in \(\R^n\), Definition
vector space, Definition Definition
basis, Definition
dimension, Definition
finite dimensional, Definition
subspace, Definition
vector spaces
isomorphic, Paragraph
Wronskian, Project Activity