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Discover Linear Algebra: A first course in linear algebra

Jeremy Sylvestre

Index Index

addition
matrix, Item
vector, Item
adjoint
classical, Discovery Item
algebraic multiplicity, Discovery Item
augmented matrix, Discovery Item
basis, Item
ordered, Item
standard, Discovery Item
Cauchy-Schwarz inequality, Theorem Theorem
characteristic
equation (for a matrix), Item
polynomial, Discovery
polynomial (for a matrix), Item
space, Note
value, Note
vector, Note
coefficient matrix, Item
cofactor, Discovery Item
expansion, Item
matrix, Discovery Item
column
in a matrix, Item
space, Discovery Item
vector, Item
component
orthogonal, Discovery
orthogonal (to a vector in \(\R^n\)), Item
parallel, Discovery
parallel (to a vector in \(\R^n\)), Item
components, Discovery Item
consistent system, Item
coordinate vector, Discovery Item Paragraph
coordinates, Discovery Item Paragraph
Cramer’s rule, Subsection
cross product, Item Paragraph
determinant, Paragraph Discovery
matrix, Item
minor, Discovery Item
diagonal matrix, Item Item
diagonalizable, Item
dimension, Item
directed line segment, Discovery Item
dot product, Discovery
real, Item
eigenspace, Discovery
matrix, Item
eigenvalue
matrix, Item
multiplicity
algebraic, Discovery Item
geometric, Discovery Item
eigenvector, Discovery
matrix, Item
elementary
matrix, Paragraph Item
row operations, Item
entry (of a matrix), Item
equation(s)
linear, Item
parametric, Item
system of, Item
Euclidean
inner product, Discovery Item
finite-dimensional, Item Item
free variables, Item
general solution, Item
geometric multiplicity, Discovery Item
homogeneous system, Discovery Item
identity matrix, Item
inconsistent system, Item
inequality
Cauchy-Schwarz, Theorem Theorem
triangle, Theorem
initial point, Discovery Item
inner product
Euclidean, Discovery Discovery Item
standard, Item
inverse (of a matrix), Item
invertible, Discovery
matrix, Item
leading
one, Item
variables, Item
linear
combination, Paragraph Discovery Item
of vectors, Item
equation, Item
linearly
dependent, Discovery Item
independent, Discovery Item
lower triangular matrix, Item Item
main diagonal, Item Paragraph
matix
diagonal, Item Item
lower triangular, Item Item
symmetric, Item Item
upper triangular, Item Item
matrix, Item
addition, Item
adjoint (classical), Discovery Item
augmented, Discovery Item
characteristic equation, Item
characteristic polynomial, Item
coefficient, Item
cofactor, Discovery Item
cofactor expansion, Item
column, Item
column space, Discovery Item
determinant, Discovery Item
diagonalizable, Item
dimensions, Discovery Item
eigenspace, Item
eigenvalue, Item
eigenvector, Item
elementary, Item
entry, Item Item
equality, Item
identity, Item
inverse, Item
invertible, Item
minor, Discovery Item
nilpotent, Paragraph
null space, Paragraph Item
nullity, Item
of cofactors, Discovery Item
row, Item
row space, Paragraph Item
scalar, Item Item
scalar multiple, Item
similarity, Item
singular, Item
size, Discovery Item
square, Item
transition, Discovery Item
transpose, Item
unipotent, Paragraph
Vandermonde, Item
zero, Item
minor, Discovery Item
multiplicity
algebraic, Discovery Item
geometric, Discovery Item
nilpotent
matrix, Paragraph
nontrivial solution, Item
norm, Discovery
in \(\R^n\), Item
normal vector, Discovery Item
normalization, Item
null
space, Paragraph Item
nullity
of a matrix, Item
ordered basis, Item
orthogonal
component, Discovery
component (to a vector in \(\R^n\)), Item
projection, Discovery
projection (onto a vector in \(\R^n\)), Item
vectors, Discovery
vectors (in \(\R^n\)), Item
parallel
component, Discovery
component (to a vector in \(\R^n\)), Item
vectors, Item
parallel vectors, Paragraph
parallelogram rule, Paragraph
parametric equations, Item
point-normal form
for a line, Discovery Item Paragraph
for a plane, Item
point-parallel form
for a line, Item
for a plane, Item
projection, Discovery
onto a vector in \(\R^n\), Item
rank
of a matrix, Item
right-hand rule, Paragraph
row
echelon form, Item
reduced, Item
equivalent, Item
in a matrix, Item
reduction, Item
space, Paragraph Item
vector, Item
row operations
elementary, Item
scalar, Item Item Item
matrix, Item Item
multiple
of a matrix, Item
of a vector, Item
multiplication
abstract (real), Item
similar matrices, Item
singular, Discovery
matrix, Item
size (of a matrix), Item
solution
general, Item
nontrivial, Item
set, Item
space, Item
to a system of linear equations, Item
trivial, Item
span, Discovery Item
spanning
set, Item
square matrix, Item
standard
basis, Discovery
basis vectors, Item
inner product, Discovery Item
subspace, Item
generated, Item
test, Paragraphs Procedure Proposition
Subspace Test, Paragraphs Procedure Proposition
symmetric matrix, Item Item
system
consistent, Item
homogeneous, Discovery Item
inconsistent, Item
of linear equations, Item
solution, Item
terminal point, Discovery Item
transition matrix, Discovery Item
transpose, Item
triangle inequality, Theorem
trivial
solution, Item
subspace, Item
vector space, Item
unipotent matrix, Paragraph
unit vector, Discovery
in \(\R^n\), Item
upper triangular matrix, Item Item
Vandermonde matrix, Item
vector, Discovery Item
abstract, Item Definition
addition, Item Item
angle (in \(\R^n\)), Item
column, Item
components, Discovery Item
coordinate, Discovery Item Paragraph
coordinates, Discovery Item Paragraph
cross product, Item Paragraph
distance, Item
initial point, Discovery Item
length, Item
linear combination, Item
magnitude, Item
negative, Item Item
norm, Discovery
norm (in \(\R^n\)), Item
normal, Discovery Item
normalization, Item
of constants, Item
of unknowns, Item
orthogonal, Discovery
orthogonal (in \(\R^n\)), Item
parallel, Item Paragraph
row, Item
scalar multiple, Item
space, Definition
basis, Item
dimension, Item
finite-dimensional, Item
infinite-dimensional, Item
trivial, Item
space (real), Item
standard basis, Discovery Item
subtraction, Item Item
terminal point, Discovery Item
unit, Discovery
unit (in \(\R^n\)), Item
zero, Item
zero
matrix, Item
vector, Item Item
space, Item
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