Any-n-×-n-permutation-matrix-can-be-constructed-as

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Any and n

* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.

Any subset of R n ( with its subspace topology ) that is homeomorphic to another open subset of R n is itself open.

Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.

Any orthogonal matrix of size n × n can be constructed as a product of at most n such reflections.

Any rotation matrix of size n × n can be constructed as a product of at most n ( n − 1 )/ 2 such rotations.

Any n × n matrix A of the form

To show that U ( n ) is connected, recall that any unitary matrix A can be diagonalized by another unitary matrix S. Any diagonal unitary matrix must have complex numbers of absolute value 1 on the main diagonal.

# Any smooth manifold of dimension n ≥ 3 admits a Riemannian metric with negative Ricci curvature.

for some p between 1 and n. Any two such expressions of q ( at the same point m of M ) will have the same number p of positive signs.

* Any positive multiple of the repunit R n ( b ) contains at least n nonzero digits in base b.

Any covering space of a differentiable manifold may be equipped with a ( natural ) differentiable structure that turns p ( the covering map in question ) into a local diffeomorphism – a map with constant rank n.

Any n × n real symmetric matrix A determines a quadratic form q A in n variables by the formula

Any and ×

Any conjectures are largely based on the date of her father's death ( 1006 ), the approximate date of her betrothal to Cnut ( 1004 × 1016, see below ) and the time by which she had borne him sons, whose ages are themselves difficult to establish.

* Any two objects X and Y of C have a product X × Y in C.

Any one of these decompositions, or Lie algebra renderings, may be necessary for rendering the Lie subalgebra of a 2 × 2 real matrix.

Any 2 × 2 matrix can be written in the form, where I is the identity matrix, σ i are the Pauli matrices and u is a unit vector.

Any and permutation

Any simplicial automorphism φ of X defines a permutation π of Z / n Z such that label ( φ ( M ))

Any permutation of the corners is possible, including odd permutations.

Any permutation of the edges is possible, including odd permutations, giving 24!

Any permutation of the eight corners is possible ( 8!

Any permutation of the corners is possible, including odd permutations, giving 8!

Any permutation of the outer edges is possible, including odd permutations, giving 24!

Lemma: Any linear code is permutation equivalent to a code which is in standard form.

Any and matrix

* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.

Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:

* Any square matrix with unit Euclidean norm is the average of two unitary matrices.

Any invertible matrix can be uniquely represented according to the polar decomposition as the product of a unitary matrix and a hermitian matrix with positive eigenvalues.

Any square diagonal matrix is also a symmetric matrix.

Any square matrix can be viewed as the adjacency matrix of a weighted directed graph, with representing the weight of the arc from vertex i to vertex j.

Any symmetric matrix A can be transformed into a diagonal matrix

Any solution of the above set of equations following the constraints for is defined as the factors, and as the loading matrix.

Any real square matrix A may be decomposed as

If the operator is originally given by a square matrix M, then its Jordan normal form is also called the Jordan normal form of M. Any square matrix has a Jordan normal form if the field of coefficients is extended to one containing all the eigenvalues of the matrix.

Any and can

He merely said, `` Any good decorator these days can make you a tasteful home ''.

Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.

Any needy family living in San Francisco can obtain toys by writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex of each child in the family between the ages of 1 and 12.

Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.

Any use of antibiotics can increase selective pressure in a population of bacteria to allow the resistant bacteria to thrive and the susceptible bacteria to die off.

* Any ring A can be considered as a Z-algebra in a unique way.

Any of these body styles can optionally incorporate a " cutaway ".

Any Latin-American country can join the 1980 Montevideo Treaty.

Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.

Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.

Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.

Any of these ways can be criticized for ...

* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.

Any Sangiovese-based wine made according to the Chianti guidelines from these vineyards can be labelled and marked under the basic Chianti DOCG should the producer wish to use the designation.

Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.

Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.

Any person who uses the Spanish title of " Doctor " ( or " Dr .") without being included in this Government database can be prosecuted for fraud.

Any player on the kicking team behind the kicker, and including the kicker, can recover the kick.

Any sound that can be sampled can be used.

Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.

# Any real number can be added to both sides.

# Any real number can be subtracted from both sides.

# Any real number can be multiplied to both sides.

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