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 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 maximally symmetric space has constant curvature.

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 self-adjoint operator is maximal symmetric.

Every self-adjoint operator is densely defined, closed and symmetric.

Every connected symmetric graph must thus be both vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree.

Every symmetric association scheme is commutative.

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 physical quantity has a Hermitian linear operator associated to it, and the states where the value of this physical quantity is definite are the eigenstates of this linear operator.

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 operator also received 80 hours of medical training.

Every delta operator ' has a unique sequence of " basic polynomials ", a polynomial sequence defined by three conditions:

Every motion of the lock is derived from movement of the hands rather than elements beyond the operator ’ s control, such as dirt, rust, or memory.

* Every first time purchaser of an automobile deprived the streetcars operator of income whilst simultaneously created additional traffic congestion which often reduced service speeds and thereby increased their operational costs and making the services less attractive to the remaining users.

Is fundamental for the many-body theory that Every operator can be expressed in terms of annihilation and creation operators.

Every operator can then route calls directly to their own customers, or pass them on to another operator if the call is not for one of their customers.

Every closure operator on a poset has many fixed points ; these are the " closed elements " with respect to the closure operator, and they are the main reason the closure operator was defined in the first place.

Every self-adjoint operator is normal.

Every operator in the unit is cross-trained in a variety of " low-visibility " skills such as weapons, survival, sniping, medic, small boat handling, driving, tracking, air ops etc.

where the rank refers to the rank of the linear operator F. Every nonsimple bivector can be written as a sum of at most two simple ones.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

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 taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.