INDEX

A

• addition, column matrix
• addition, of matrices
• addition, point + vector
• addition, zero matrix
• angle between non-unit vectors
• angle between two 3D non-unit vectors
• angle between two 3D unit vectors
• angle, between unit vectors
• associative property, vector addition
• axis

C

• change of frames
• column matrix
• column matrix addition, associative
• column matrix addition, commutative
• column matrix flipping in matrix product
• column matrix subtraction, non-commutative
• commutative property, vector addition
• computer graphics, activities
• conformant, matrices
• conformant, matrices
• coordinate frame
• coordinate frame
• coordinates, determining
• cosine, and unit circle
• cosine, angles which yield negative values
• cross product, anti-commutative
• cross product, as area of parallelogram
• cross product, as determinant
• cross product, between coordinate axes
• cross product, colinear vectors
• cross product, computing
• cross product, definition
• cross product, distributive property
• cross product, not associative
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• cross product, properties (summary)
• cross product, with zero vector

D

• determinant
• determinant of singular matrix
• determinant, evaluation
• determinant, two rows the same
• dimensions
• displacement
• displacement, formula
• dot prodcut, column matrix with self
• dot product of column matrices
• dot product, 3D column matrices
• dot product, affected by vector properties
• dot product, ambiguous orientation
• dot product, and length
• dot product, and vector length
• dot product, as matrix product
• dot product, column matrices, distributive
• dot product, column matrix, commutative
• dot product, column matrix, properties
• dot product, commutative
• dot product, definition
• dot product, of orthogonal vectors
• dot product, properties

E

• element
• equality, column matrix
• equality, of matrices
• equating elements of column matrices

H

• Head-to-Tail Rule, vector addition

I

• identity matrix
• identity matrix, matrix product
• identity, transpose
• identity, unique
• inner product
• inverse inverse
• inverse of matrix product
• inverse of matrix transpose

L

• length and direction, converting to (x,y)
• length, of 3D vectors
• length, of a vector
• length, of negated vector
• length, of vector aligned with axis
• length, of vector, formula
• length, vector
• length, vector, always positive or zero
• line
• line segment

M

• matrix-matrix product, associative
• matrix-matrix product, calculation
• matrix-matrix product, distributive
• matrix-matrix product, non-commutative
• matrix-matrix product, scalar factor
• matrix column flipping in matrix product
• matrix inverse
• matrix inverse, unique
• matrix product as many dot products
• matrix product, non-commutative
• matrix product, steps
• Matrix rank
• matrix subtraction
• matrix times column matrix
• matrix times column matrix, definition
• matrix transpose
• matrix, definition
• matrix, diagonal
• matrix, identity
• matrix, names
• matrix, names
• matrix, negation
• matrix, non-singular
• matrix, singular
• matrix, square
• multiplication, matrix scalar

N

• negative column matrix
• normal, many meanings of
• normalizing a vector

O

• orientation, 2D vector formula
• orientation, of 2D vector
• origin
• orthogonal vector, creating
• orthogonal vectors, dot product

P

• parallelogram
• plane, defined by two vectors
• point
• point
• point, represented as column matrix
• points, represented as column matrix
• points, represented in different frames
• projection, fast formulae
• projection, one vector onto another
• projection, vector, formula
• projection, vector, orthogonal component
• projection, vector, procedure
• pythagorean formula

R

• radians
• representation
• right-hand rule
• row matrix times matrix
• row matrix times matrix, definition

S

• scalar
• scalar multiplication, matrix
• scalar product
• scaling, of a vector
• scaling, properties
• slope
• slopes, of perpendicular lines
• solid geometry problems, and vectors
• subtraction, column matrices

T

• terms review
• translation
• transpose
• transpose, of a column matrix
• triangle
• triangle inequality
• triangle inequality, example

U

• unit normal
• unit normals, in 3D
• unit vector
• unit vector
• unit vector, as direction
• unit vector, orientation

V

• vector
• vector
• vector addition, associative property
• vector addition, commutative property
• vector addition, in three dimensions
• vector orientation, trouble with negative components
• vector projection, 3D example
• vector, representation
• vector, represented with column matrix
• vectors, colinear

Z

• zero matrix
• zero matrix
• zero vector, addition of