Index Index
\(LU\) factorization, Example
\(LU\)factorization, Subsection
\(QR\) factorization, Subsection Activity. See also
numpy.linalg.qr()
full, Note
reduced, Note
\(R^2\). See coefficient of determination
attractor, Item
spiral, Item
augementation
of a matrix, Proposition
augementation principle, Proposition
augmentation
of a matrix, Item
axis
of an array or tensor, Paragraph
back substitution, Observation
basic variable, Item
basis, Definition
basis, of a subspace, Definition
basis, standard, Example
case, Item
centroid, Activity
channels-last convention, Example
characteristic equation, Paragraph
characteristic polynomial, Subsection Paragraph. See also
sympy.Matrix.charpoly()
charpoly(). See sympy.Matrix.charpoly()
chrominance, Paragraph
clustering, Subsection Paragraph
codomain, Paragraph
coefficient matrix, Paragraph
coefficient of determination, Definition
coefficients
of a regression equation, Paragraph
cofactor expansion, Subsubsection
color model, Paragraph
column space, Definition
column-variate form, Paragraph
column_stack(). See np.column_stack()
commutative, Paragraph
component
of a vector, Item
composition
of functions, Paragraph
consistent system, Item
correlation, Item
covariance matrix, Paragraph
data matrix, Paragraph
decoupled system, Observation
determinant, Definition
in Python, Item
of a \(2 \by 2\) matrix, Assemblage
via cofactor expansion, Subsubsection
deviation score. See demean
diagonal matrix, Definition Paragraph Exercise
diagonalizable matrix, Definition Paragraph
diagonalization
orthogonal, Definition
dimension, Definition Warning
of a vector, Item
discrete dynamical system, Paragraph
Discrete Fourier Transform, Paragraph
document vector, Item
domain, Paragraph
dominant eigenvalue, Paragraph
dot product, Definition Item
dynamical system
discrete, Paragraph
eigenspace, Paragraph
eigenvalue, Definition
dominant, Paragraph
of a triangular matrix, Proposition
eigenvector, Definition Item. See also
np.linalg.eig()
left, Item
right, Item
eignevalue
multiplicity of, Paragraph
elementary matrices
inverses of, Paragraph
elementary row operation, Paragraph
entry
of a vector, Item
evalf(). See sympy.evalf()
factorization
\(LU\), Example
free variable, Item
function composition, Paragraph
fundamental subspaces, Paragraph
Haar wavelet basis, Example
Haar wavelet transform, Example
high dynamic range (HDR) images, Example
homogeneous coordinates, Paragraph
idempotent, Item
identity matrix, Subsection Item
columns (\(\evec_j\)), Paragraph
identity transformation, Item
ill-conditioned matrix, Exercise
import, Paragraph
inconsistent system, Item
indexing, Python vectors, Paragraph
inner product, Paragraph
inverse
left, Definition
right, Definition
inverse of a matrix, Exercise
invertible matrix, Definition
kernel. See null space
left inverse. See inverse, left
left inverse of a matrix, Exercise
length
of a vector (see norm)
linalg. See scipy.linalg
linalg.det(), Item
linear combination, Definition
of vectors, Item
linear equation, Definition
linear model, Subsection Paragraph
linear system, Definition
linear system of equations, Example
linear transformation, Paragraph Proposition
linearity of matrix tranformations, Assemblage
linearity of matrix transformations, Proposition
linearly dependent, Definition
linearly independent, Definition
lower triangular matrix, Definition
luminance, Paragraph
magnitude
of a vector (see norm)
matplotlib.plt.quiver(), Paragraph
matplotlib.pyplot, Item
matrix
diagonalizable, Definition Paragraph
identity, Item
inverse, Exercise Definition
left, Exercise
positive, Definition
shape, Paragraph
similar, Exercise Definition Paragraph
stochastic, Example
stochastic matrix, Definition
symmetric, Paragraph Definition
transpose, Paragraph
matrix factorization, Paragraph
matrix transforamtion, Proposition
matrix transformation, Definition
matrix transformations
linearity of, Assemblage Proposition
matrix, addition, Paragraph
matrix, elementary, Paragraph
matrix, rank, Definition
matrix, scalar multiplication, Paragraph
matrix-vector multiplication, Definition
mean, Example
model matrix, Paragraph
model space, Paragraph
Moore-Penrose psuedoinverse, Paragraph
multiplicity
of an eigenvalue, Paragraph
n-dimensional array, Paragraph
norm
Euclidean, Item
of a vector, Subsection Definition Subsection
normal equation, Paragraph
np.column_stack(), Item
np.corrcoef(), Item
np.linalg.eigvals(), Item
np.linalg.norm(), Item
np.linalg.solve(), Paragraph
np.linalg.svd(), Paragraph
null space, Item Definition. See also
scipy.linalg.null_space()
numpy, Item
numpy.arange(), Paragraph
numpy.linalg.det(). See linalg.det()
numpy.linalg.eig(), Item. See also scipy.linalg.eig()
numpy.linalg.eigvals(), Item
numpy.linalg.norm(). See norm of a vector
numpy.linalg.qr(), Activity
numpy.mean(), Paragraph
numpy.polynomial.polynomial.polyvander(), Paragraph
numpy.random.normal(), Paragraph
numpy.round(), Paragraph
numpy.std(), Paragraph
numpy.sum(), Paragraph
observational unit, Item
onto
transformation, Paragraph
orientation
of a pair of vectors, Paragraph
origin, Item
orthogonal complement, Definition Paragraph
orthogonal diagonalization, Definition
orthogonal matrix, Definition
orthogonal set of vectors, Definition
orthogonal vectors, Definition
othonormal set, Definition
outer product, Paragraph
pandas, Item
parallelepiped, Paragraph
parametric description, Item
partial pivoting, Paragraph
phase portrait, Paragraph
pivot position, Definition
plotly, Item
polynomial
characteristic, Paragraph
positive matrix, Definition
power method, Example Subsection
principal components, Paragraph
probability vector, Definition
projection, Paragraph Proposition Item
quadratic form, Definition
quiver(). See matplotlib.plt.quiver()
range
of a transformation, Paragraph
rank, Definition
Rational(). See sympy.Rational()
reduced row echelon form, Definition
not numerically stable, Item
reduced row echelon form (RREF)
augementation principle, Proposition
reduced row echelon matrix, Definition
regression. See least squares regression
repellor, Item
spiral, Item
reshape(), Paragraph
RGB color model, Paragraph
right inverse. See inverse, right
round off error, Paragraph
row equivalent, Paragraph
row space, Paragraph
row-variate form, Paragraph
RREF. See reduced row echelon form
saddle, Item
scalar, Item
SciPy, Item
scipy.linalg, Item
scipy.linalg.det(). See linalg.det()
scipy.linalg.null_space(), Item
seaborn.objects, Item
shape
of a matrix, Paragraph
shape, of a vector, Paragraph
shear, Item
similar matrices, Exercise Definition Paragraph
singular value decomposition
computing with NumPy, Paragraph
reduced, Proposition
slice, of a matrix or tensor, Paragraph
solution space, Definition
solution to a linear system, Definition
solve(). See np.linalg.solve()
span, Definition
spiral attractor, Item
spiral repellor, Item
standard deviation, Example
state vector, Paragraph
stationary vector, Definition
steady-state vector, Definition
stochastic matrix, Definition Example
subject, Item
subspace, Definition
symmetric matrix, Paragraph Definition
sympy, Item
sympy.evalf(), Item
sympy.Matrix.charpoly(), Item
sympy.Rational(), Item
tensor, Paragraph
time series, Item
trajectory, Paragraph
transforamtion
matrix, Proposition
transition function, Paragraph
translation, Paragraph
transpose, Definition
triangular system, Observation
upper triangular matrix, Definition
Vandermonde matrix, Paragraph. See also
numpy.polynomial.polynomial.polyvander()
variable vector, Item
variance-covariance matrix. See covariance matrix
vector
plotting, Paragraph
probability, Definition
stationary, Definition
steady-state, Definition
unit (see unit vector)
vector space, Item
weights, Definition
YCbCr color model, Paragraph
