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Every real symmetric matrix is Hermitian, and therefore all its eigenvalues are real.

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## Some Related Sentences

Every and real

*

__Every____real__Banach algebra which**is**a division algebra**is**isomorphic to the reals**,**the complexes**,**or the quaternions**.**
*

__Every__unital__real__Banach algebra with no zero divisors**,****and**in which every principal ideal**is**closed**,****is**isomorphic to the reals**,**the complexes**,**or the quaternions**.**
*

__Every__commutative__real__unital Noetherian Banach algebra with no zero divisors**is**isomorphic to the__real__or complex numbers**.**
*

__Every__commutative__real__unital Noetherian Banach algebra ( possibly having zero divisors )**is**finite-dimensional**.**__Every__sequence that ran off to infinity in the

__real__line will then converge to ∞ in this compactification

**.**

__Every__holomorphic function can be separated into

**its**

__real__

**and**imaginary parts

**,**

**and**each of these

**is**a solution of Laplace's equation on R < sup > 2 </ sup >.

__Every__ordered field

**is**a formally

__real__field

**,**i

**.**e., 0 cannot be written as a sum of nonzero squares

**.**

*

__Every__separable metric space**is**isometric to a subset of the ( non-separable ) Banach space l < sup >∞</ sup > of**all**bounded__real__sequences with the supremum norm ; this**is**known as the Fréchet embedding**.**__Every__non-negative

__real__number a has a unique non-negative square root

**,**called the principal square root

**,**which

**is**denoted by

**,**where √

**is**called the radical sign or radix

**.**

__Every__nonzero

__real__number has a multiplicative inverse ( i

**.**e

**.**an inverse with respect to multiplication ) given by ( or ).

__Every__sedenion

**is**a

__real__linear combination of the unit sedenions 1

**,**< var > e </ var >< sub > 1 </ sub >, < var > e </ var >< sub > 2 </ sub >, < var > e </ var >< sub > 3 </ sub >, ...,

**and**< var > e </ var >< sub > 15 </ sub >,

__Every__Riemann surface

**is**a two-dimensional

__real__analytic manifold ( i

**.**e., a surface ), but it contains more structure ( specifically a complex structure ) which

**is**needed for the unambiguous definition of holomorphic functions

**.**

In his book Nirvana: The Stories Behind

__Every__Song**,**Chuck Crisafulli writes that the song " stands out in the Cobain canon as a song with a very specific genesis**and**a very__real__subject ".__Every__finite or bounded interval of the

__real__numbers that contains an infinite number of points must have at least one point of accumulation

**.**

Every and symmetric

__Every__Boolean algebra ( A

**,**∧, ∨) gives rise to a ring ( A

**,**+, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation

**is**called

__symmetric__difference in the case of sets

**and**XOR in the case of logic )

**and**a · b := a ∧ b

**.**The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring

**is**the 1 of the Boolean algebra

**.**

__Every__

__symmetric__graph without isolated vertices

**is**vertex-transitive

**,**

**and**every vertex-transitive graph

**is**regular

**.**

__Every__

__symmetric__group has a one-dimensional representation called the trivial representation

**,**where every element acts as the one by one identity

**matrix**

**.**

__Every__connected

__symmetric__graph must thus be both vertex-transitive

**and**edge-transitive

**,**

**and**the converse

**is**true for graphs of odd degree

**.**

__Every__convex centrally

__symmetric__polyhedron P in R < sup > 3 </ sup > admits a pair of opposite ( antipodal ) points

**and**a path of length L joining them

**and**lying on the boundary ∂ P of P

**,**satisfying

Every and matrix

__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__constraint

**is**in turn a pair ( usually represented as a

__matrix__), where

**is**an-tuple of variables

**and**

**is**an-ary relation on

**.**

*

__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

**.**

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