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Page "Eigenvalues and eigenvectors" ¶ 88
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Every and eigenvalue
Every spin network is an eigenstate of each such operator, and the area eigenvalue equals
Every generalized eigenvalue of a normal operator is thus genuine.
Every eigenvalue of T belongs to σ ( T ), but σ ( T ) may contain non-eigenvalues.

Every and matrix
< li > Every positive definite matrix is invertible and its inverse is also positive definite.
Every aspect of the line matrix printer is designed to deliver higher reliability, fast throughput, and greater resistance to rough handling and hazardous environmental conditions.
Every diagonal matrix is symmetric, since all off-diagonal entries are zero.
Every symmetric matrix is thus, up to choice of an orthonormal basis, a diagonal matrix.
Every real symmetric matrix is Hermitian, and therefore all its eigenvalues are real.
Every orthogonal matrix has determinant either 1 or − 1.
Every symplectic matrix is invertible with the inverse matrix given by
Every Hermitian matrix is a normal matrix, and the finite-dimensional spectral theorem applies.
Every constraint is in turn a pair ( usually represented as a matrix ), where is an-tuple of variables and is an-ary relation on.
Every hypergraph has an incidence matrix where
Every real m-by-n matrix yields a linear map from R < sup > n </ sup > to R < sup > m </ sup >.
* Every finite-dimensional simple algebra over R must be a matrix ring over R, C, or H. Every central simple algebra over R must be a matrix ring over R or H. These results follow from the Frobenius theorem.
* Every finite-dimensional simple algebra over C must be a matrix ring over C and hence every central simple algebra over C must be a matrix ring over C.
* Every finite-dimensional central simple algebra over a finite field must be a matrix ring over that field.
We call a field E a splitting field for A if A ⊗ E is isomorphic to a matrix ring over E. Every finite dimensional CSA has a splitting field: indeed, in the case when A is a division algebra, then a maximal subfield of A is a splitting field.
* Every 4-dimensional central simple algebra over a field F is isomorphic to a quaternion algebra ; in fact, it is either a two-by-two matrix algebra, or a division algebra.
Every object in the drawing can be subjected to arbitrary affine transformations: moving, rotating, scaling, skewing and a configurable matrix.
Every pixel from the secret image is encoded into multiple subpixels in each share image using a matrix to determine the color of the pixels.

Every and has
Every soldier in the army has, somewhere, relatives who are close to starvation.
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every calculation has been made independently by two workers and checked by one of the editors.
Every retiring person has a different situation facing him.
Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
`` Every woman in the block has tried that ''.
: Every set has a choice function.
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** Every surjective function has a right inverse.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every vector space has a basis.
* Every small category has a skeleton.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
** Every field has an algebraic closure.
** Every field extension has a transcendence basis.
** Every Tychonoff space has a Stone – Čech compactification.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.

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