Index Index
\(\in\), Item
\(\notin\), Item
\(x\)-axis, Paragraph
\(x\)-coordinate, Paragraph
\(y\)-axis, Paragraph
\(y\)-coordinate, Paragraph
abscissa, Paragraph
absolute value, Paragraphs
adjugate, Item
antisymmetric, Definition
augmented matrix, Paragraph
Cartesian coordinate plane, Paragraph
Cartesian coordinates, Paragraph
characteristic polynomial, Definition Definition
cofactor, Definition
expansion, Definition Theorem
matrix, Item
column
pivot, Paragraph
column space, Definition
column vector, Definition
complex conjugate
definition of, Paragraph
properties of, Theorem
Complex Factorization Theorem, Theorem
complex number
definition of, Definition
complex numbers, Paragraph
addition, Definition
equality, Definition
multiplication, Definition
conjugate of a complex number
properties of, Theorem
consistent, Definition Key Idea Key Idea
coordinates
Cartesian, Paragraph
Cramer’s Rule, Theorem
cross product
applications, Paragraph
applications!area of parallelogram, Paragraphs
applications!torque, Paragraphs
applications!volume of parallelepiped, Paragraphs
definition, Definition
dependent
linear, Paragraph
determinant
and elementary row operations, Theorem
definition, Definition
of \(2\times 2\) matrices, Definition
of triangular matrices, Key Idea
properties, Theorem
diagonal
definition, Definition
diagonalizable matrix, Definition
diagonalization, Paragraphs
orthogonal, Paragraphs
diagram
Venn Diagram, Paragraph
dimension, Definition
distance
between point and plane, Paragraph
between points in space, Definition
definition, Paragraphs
distance formula, Key Idea
dot product
definition, Definition
eigenspace, Definition
eigenvalue
definition, Definition
finding, Key Idea
properties, Theorem
eigenvector
see: eigenvalue, Definition
elementary matrix, Definition
elementary operation, Paragraph
elementary row operation, Paragraph
elementary row operations, Key Idea
and determinants, Theorem
empty set, Definition
equivalence relation, Paragraphs
factorization
over the complex numbers, Theorem
first octant, Paragraph
Fundamental Theorem of Algebra, Theorem
Head To Tail Rule, Paragraph
homogeneous, Definition Key Idea Key Idea
identity matrix, Definition
imaginary unit, Paragraph
inconsistent, Definition
independent
linear, Paragraph
initial point, Definition
intersection of two sets, Item
inverse
computing, Key Idea
definition, Definition
Invertible Matrix Theorem, Theorem
uniqueness, Theorem
Jordan Canonical Form, Paragraphs
leading one, Definition Key Idea Key Idea
linear combination, Definition Definition
linear equation, Definition
linear transformation
and zero, Key Idea
conditions on, Key Idea
definition, Definition
standard matrix of, Definition Theorem
linearly dependent, Paragraph
linearly independent, Paragraph
lines, Paragraph
equations for, Definition
intersecting, Paragraph
parallel, Paragraph
skew, Paragraph
magnitude of vector, Definition
matrix
addition, Definition
adjugate, Item
arithmetic properties, Theorem
augmented, Paragraph
cofactor, Definition Item
definition, Definition
determinant, Definition Definition
diagonal, Definition
diagonalizable, Definition
elementary, Definition
equality, Definition
identity matrix, Definition
inverse, Definition Key Idea
minor, Definition
multiplication, Definition
multiplication!properties, Theorem
of coefficients, Paragraph
scalar multiplication, Definition
similar, Definition
the zero matrix, Definition
transpose, Definition
triangular, Definition
matrix transformation, Paragraph
midpoint
definition of, Paragraphs
midpoint formula, Key Idea
minor, Definition
multiplicity
algebraic, Definition
and diagonalization, Theorem
geometric, Definition
of an eigenvalue, Paragraphs
octant
first, Paragraph
ordered pair, Paragraph
ordinate, Paragraph
origin, Paragraph
orthogonal, Definition
decomposition, Key Idea
orthogonal decomposition of vectors, Key Idea
orthogonal projection, Definition
parallel vectors, Definition
Parallelogram Law, Paragraph
particular solution, Definition
perpendicular|see{orthogonal}, Definition
pivot column, Paragraph
planes
coordinate plane, Paragraph
distance between point and plane, Paragraph
equations of, Definition
introduction, Paragraph
normal vector, Paragraph
problem solving, Key Idea
pseudoinverse, Paragraph
quadrants, Paragraph
r@\(\mathbb{R}\), Paragraph
range
of a linear transformation, Paragraph
rank
in terms of column space, Paragraph
in terms of leading 1s, Definition
reduced echelon form, Definition
reduced row echelon form, Definition
relatively prime, Example
right hand rule
of Cartesian coordinates, Paragraph
of the cross product, Paragraphs
row echelon form, Definition
row vector, Definition
scalar, Section
set
definition of, Definition
empty, Definition
exclusion, Item
inclusion, Item
intersection, Item
roster method, Item
set-builder notation, Item
union, Item
verbal description, Item
set-builder notation, Item
similar matrices, Definition
properties of, Theorem
skew symmetric, Paragraph
definition, Definition
theorem, Theorem
solution, Definition
basic, Definition
general, Example
infinite, Theorem
none, Theorem
particular, Example Definition
types, Theorem
span, Definition Definition
standard unit vector, Definition
subset
definition of, Definition
subspace, Definition
span, Theorem
trivial, Paragraph
symmetric, Paragraph
definition, Definition
theorem, Theorem
system of linear equations
consistent, Definition Key Idea Key Idea Key Idea
definition, Definition
homogeneous, Definition
inconsistent, Definition Key Idea
solution, Definition
terminal point, Definition
theorem
Fundamental Theorem of Algebra, Theorem
torque, Paragraphs
trace
definition, Definition
properties, Theorem
transformation
matrix, Paragraph
transpose, Paragraph
definition, Definition Definition
properties, Theorem
skew-symmetric, Definition
symmetric, Definition
triangular matrix
definition, Definition
determinant, Key Idea
variable
basic, Item
dependent, Item
independent, Item
leading, Example
vector
column, Definition
row, Definition
vector space, Paragraph
of column vectors, Definition
vectors, Definition
algebra of, Item
algebraic properties, Theorem
component form, Definition
cross product, Definition Theorem Theorem
definition, Definition
dot product, Definition Theorem Theorem
Head To Tail Rule, Paragraph
magnitude, Definition
norm, Definition
normal vector, Paragraph
orthogonal, Definition
orthogonal decomposition, Key Idea
orthogonal projection, Definition
parallel, Definition
Parallelogram Law, Paragraph
resultant, Paragraph
standard unit vector, Item
unit vector, Definition Item
zero vector, Paragraph
Venn Diagram, Paragraph
work, Definition
zero matrix, Definition
