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## Index

absolute value of a vector
Vectors
affine mapping
Mappings and symmetry operations
affine space
Points and their coordinates
angle
calculation of
Distances and angles
angle of rotation
The geometric meaning of
associative
Vectors | Rules for matrix calculations | Combination and reversion of
augmented column
( ) matrices
augmented matrix
( ) matrices
axis
of rotation
Isometries | The geometric meaning of
of rotoinversion
Isometries | The geometric meaning of
basis
Vector coefficients
conventional
The scalar product and
orthonormal
The scalar product and
primitive
The scalar product and | Space-group operations
basis vectors
Vector coefficients
Cartesian coordinates
Special coordinate systems: Cartesian
center of inversion
Isometries
centered lattice
The scalar product and
coefficients of a vector
Vector coefficients
column index
The matrix formalism
column matrix
The matrix formalism
column, augmented
( ) matrices
commutative
Vectors | Rules for matrix calculations
conventional basis
The scalar product and
coordinate axes
Points and their coordinates
coordinate system
Points and their coordinates
coordinate transformation
Points and their coordinates | Coordinate transformations | General coordinate transformations
coordinates
Cartesian
Special coordinate systems: Cartesian
parallel
Points and their coordinates | Special coordinate systems: Cartesian
crystal class
Crystallographic groups
crystal pattern
The scalar product and
crystallographic symmetry operation
The geometric meaning of
dependent, linearly
Vectors
determinant
The geometric meaning of
diagonal matrix
The matrix formalism
dimension
Vectors
distance
calculation of
Distances and angles | Distances and angles | Distances and angles
distributive
Rules for matrix calculations
Euclidean space
Points and their coordinates
finite group
Crystallographic groups
fixed point
Isometries | The geometric meaning of
fundamental matrix
Distances and angles
general position
The General Position' in | The General Position' in
glide part
The geometric meaning of
glide plane
Isometries
glide reflection
Isometries | Space-group operations | The geometric meaning of
glide vector
Isometries | The geometric meaning of
group
finite
Crystallographic groups
infinite
Crystallographic groups
order of a
Crystallographic groups
Hermann-Mauguin symbol
Crystallographic site-symmetry operations
HM symbol
Crystallographic site-symmetry operations
identity
Isometries | Combination and reversion of | The geometric meaning of
image
Mappings and symmetry operations
improper isometry
Isometries
independent, linearly
Vectors
indices notation
Rules for matrix calculations
infinite group
Crystallographic groups
integer matrix
The matrix formalism | The matrix-column pairs of
intrinsic translation part
The geometric meaning of
intrinsic translation part
The geometric meaning of
inverse matrix
Inversion of a matrix
inversion
Isometries | Crystallographic site-symmetry operations | The geometric meaning of
center of
Isometries | The geometric meaning of
isometric mapping
Mappings and symmetry operations
isometry
Mappings and symmetry operations | Isometries
first kind
Mappings and symmetry operations | Isometries
improper
Isometries
order of
Crystallographic site-symmetry operations
proper
Isometries
second kind
Isometries
IT A
List of symbols
lattice
centered
The scalar product and
primitive
The scalar product and
lattice basis
The scalar product and
primitive
The scalar product and
lattice constants
The scalar product and
lattice vector
The scalar product and
law
associative
Vectors
commutative
Vectors
law of composition
Combination and reversion of
length of a vector
Vectors
linear combination
Vector coefficients
linearly dependent
Vectors
linearly independent
Vectors
location part
The geometric meaning of
mapping
Mappings and symmetry operations
affine
Mappings and symmetry operations
isometric
Mappings and symmetry operations
non-singular
Combination and reversion of
regular
Combination and reversion of
matrix
The matrix formalism
augmented
( ) matrices
diagonal
The matrix formalism
fundamental
Distances and angles
integer
The matrix formalism | The matrix-column pairs of
inverse
Inversion of a matrix
orthogonal
Inversion of a matrix
rational
The matrix formalism
regular
Determinants
singular
Determinants
symmetric
The matrix formalism
transposed
The matrix formalism
unit
The matrix formalism
matrix notation
Motivation
matrix product
Rules for matrix calculations
matrix-column pair
Rules for matrix calculations | Matrix-column pairs
mirror plane
Isometries
motion
Mappings and symmetry operations
rigid
Mappings and symmetry operations
multiplication table
Determination of the matrix-column -fold
Crystallographic site-symmetry operations
non-singular mapping
Combination and reversion of
O-matrix
The matrix formalism
o-vector
Vectors
orbit of points
The General Position' in
order of a group
Crystallographic groups
order of an isometry
Crystallographic site-symmetry operations
origin
Points and their coordinates
orthogonal matrix
Inversion of a matrix
orthonormal basis
The scalar product and
parallel coordinates
Points and their coordinates | Special coordinate systems: Cartesian
parallelogram of forces
Vectors
point group
Crystallographic site-symmetry operations | Crystallographic groups | Crystallographic groups
point lattice
Change of basis
point orbit
The General Position' in
point space
Points and their coordinates
position
general
The General Position' in | The General Position' in
special
The General Position' in
primitive basis
The scalar product and
primitive lattice
The scalar product and
primitive lattice basis
The scalar product and | Space-group operations
product of matrices
Rules for matrix calculations
projection
Mappings and symmetry operations | Combination and reversion of
proper isometry
Isometries
rational matrix
The matrix formalism
reduced operation
The geometric meaning of
reflection
Isometries | Crystallographic site-symmetry operations | The geometric meaning of
reflection plane
Isometries
regular mapping
Combination and reversion of
regular matrix
Determinants
reverse operation
Combination and reversion of
rigid motion
Mappings and symmetry operations
rotation
Isometries | Crystallographic site-symmetry operations | The geometric meaning of | The geometric meaning of
rotation angle
Isometries | The geometric meaning of
rotation axis
Isometries | The geometric meaning of
rotoinversion
Isometries | Crystallographic site-symmetry operations | Display of crystallographic symmetry | The geometric meaning of
rotoinversion axis
Isometries | The geometric meaning of
row index
The matrix formalism
row matrix
The matrix formalism
scalar product
Points and their coordinates | The scalar product and
screw axis
Isometries
screw part
The geometric meaning of
screw rotation
Isometries | Space-group operations | The geometric meaning of
screw vector
Isometries | Space-group operations | The geometric meaning of
Seitz notation
Matrix-column pairs
singular matrix
Determinants
site symmetry
Crystallographic site-symmetry operations | Crystallographic site-symmetry operations
space
affine
Points and their coordinates
point
Points and their coordinates
vector
Vectors
space group
Crystallographic site-symmetry operations | Crystallographic groups
space-group type
Crystallographic groups | The General Position' in
special position
The General Position' in
square matrix
The matrix formalism
subgroup
Crystallographic groups
symbol, Hermann-Mauguin
Crystallographic site-symmetry operations
symmetric matrix
The matrix formalism
symmetry
Mappings and symmetry operations
symmetry element
Display of crystallographic symmetry
symmetry operation
Mappings and symmetry operations | Display of crystallographic symmetry
crystallographic
Mappings and symmetry operations | The geometric meaning of
symmorphic
Crystallographic groups
trace
The geometric meaning of
translation
The scalar product and | Mappings and symmetry operations | Isometries | The geometric meaning of
translation part, intrinsic
The geometric meaning of | The geometric meaning of
translation vector
The scalar product and | Isometries
transposed matrix
The matrix formalism
type of space groups
Crystallographic groups | The General Position' in
unit cell
The volume of the
unit matrix
The matrix formalism
unit vector
Vectors
vector
Vectors
length of
Vectors
translation
The scalar product and | Isometries
unit
Vectors
vector coefficients
Vector coefficients
vector lattice
The scalar product and
vector space
Vectors
volume of the unit cell
The volume of the