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where is the adjoint of V. If T is a self-adjoint operator, then the compression is also self-adjoint.
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where and is
But California is where we're goin ''.
He thought of the jungles below him, and of the wild, strange, untracked beauty there and he promised himself that someday he would return, on foot perhaps, to hunt in this last corner of the world where man is sometimes himself the hunted, and animals the lords.
Now I wish to enter the American market, where the competition is very strong.
from downstream, where the water level is much lower, it is a high, elaborately facaded pavilion.
The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.
Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.
Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.
A dominant motive is the poet's longing for his homeland and its boyhood associations: `` Not men-folk, but the fields where I would stray, The stones where as a child I used to play ''.
In a society where everything is for sale, Marlowe is the only man who cannot be bought.
This is done for simplicity of commands and to bring the hidden redundancy up to where misunderstanding has almost zero possibility.
As to benefits to employees, it is notorious for its callous disregard except where it depends on them for services.
`` The Moral Creed '' and `` The Will To Risk '' live happily together, if we do not examine where the line is to be drawn.
Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.
Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.
She was exposing herself to temptation which it is best to avoid where it can consistently be done.
Such performance is a great tribute to American scientists and engineers, who in the past five years have had to telescope time and technology to develop these long-range ballistic missiles, where America had none before.
but it is perennially restructured in situations where anchors are dragged or lost.
`` History has this in common with every other science: that the historian is not allowed to claim any single piece of knowledge, except where he can justify his claim by exhibiting to himself in the first place, and secondly to any one else who is both able and willing to follow his demonstration, the grounds upon which it is based.
Finally we may note that the idea appears in educational theory where its influence is at present widespread.
where and adjoint
Just as kets and bras can be transformed into each other ( making into ) the element from the dual space corresponding with is where A < sup >†</ sup > denotes the Hermitian conjugate ( or adjoint ) of the operator A.
where is the quark field, a dynamical function of space-time, in the fundamental representation of the SU ( 3 ) gauge group, indexed by ; are the gluon fields, also a dynamical function of space-time, in the adjoint representation of the SU ( 3 ) gauge group, indexed by a, b, ....
An automorphism of a Lie algebra is called an inner automorphism if it is of the form Ad < sub > g </ sub >, where Ad is the adjoint map and g is an element of a Lie group whose Lie algebra is.
In this situation, F is called the lower adjoint of G and G is called the upper adjoint of F. Mnemonically, the upper / lower terminology refers to where the function application appears relative to ≤; the term adjoint relates the Galois connections to the notion with the same name from category theory as discussed further below.
In mathematics, on a finite-dimensional inner product space, a self-adjoint operator is an operator that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.
where U < sup >∗</ sup > is the adjoint of U, and I: H → H is the identity operator.
restricted to E, where d is the Cartan exterior derivative and d * is its adjoint.
A Hopf subalgebra A is said to be right normal in a Hopf algebra H if it satisfies the condition of stability, for all h in H, where the right adjoint mapping is defined by for all a in A, h in H. Similarly, a Hopf subalgebra A is left normal in H if it is stable under the left adjoint mapping defined by.
The most general setting for a free object is in category theory, where one defines a functor, the free functor, that is the left adjoint to the forgetful functor.
As is the case for all Hopf algebras, U < sub > q </ sub >( G ) has an adjoint representation on itself as a module, with the action being given by where.
where A * is the adjoint operator of A defined by
where the left hand side is the S-module of all R-linear derivations from S to M. As in the case of adjoint functors ( though this isn't an adjunction ), this is more than just an isomorphism of modules ; it commutes with S-module homomorphisms M → M and hence is an isomorphism of functors.
is formally similar to the defining properties of pairs of adjoint functors in category theory, and this is where adjoint functors got their name from.
The Lagrangian for the ghost fields in Yang – Mills theories ( where is an index in the adjoint representation of the gauge group ) is given by
In quantum field theory, the Dirac adjoint of a Dirac spinor is defined to be the dual spinor, where is the time-like gamma matrix.
N * T, where N * denotes the adjoint of N.
In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator acting between Hilbert spaces X and Y, are the square roots of the eigenvalues of the nonnegative self-adjoint operator ( where T * denotes the adjoint of T ).
The forgetful functor U: Grp → Set have a left adjoint given by the composite KF: Set → Mon → Grp where F is the free functor.
where is the pullback of forms along the right-translation in the group and is the adjoint action on the Lie algebra.
where I < sub > ad </ sub > is the Dynkin index of the adjoint representation of g. Here
where and V
If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
The photocathode sensitivities S, phosphor efficiencies P, and anode potentials V of the individual stages shall be distinguished by means of subscripts 1, and 2, in the text, where required.
where P is pressure, V is specific or molar volume, and
Alexios attempted to organize a resistance to the new regime from Adrianople and then Mosynopolis, where he was joined by the later usurper Alexios V Doukas Mourtzouphlos in April 1204, after the definitive fall of Constantinople to the crusaders and the establishment of the Latin Empire.
The refugees reached Mosynopolis, the base of the deposed emperor Alexios III Angelos, where they were initially well received, and Alexios V married Eudokia Angelina.
The pirates had raided the Danish coasts during the civil war of Sweyn III, Canute V, and Valdemar, to the point where at the accession of Valdemar one-third of Denmark lay wasted and depopulated.
*( V, x ) where x is a value of unspecified nature ; and
As in so many programming languages, the operation ( V, x ) is often written V ← x ( or some similar notation ), and ( V ) is implied whenever a variable V is used in a context where a value is required.
where R < sub > i </ sub > is the position vector of particle i from the reference point, m < sub > i </ sub > is its mass, and V < sub > i </ sub > is its velocity.
Regulatory Arbitrage was used for the first time in 2005 when it was applied by Scott V. Simpson, a partner at law firm Skadden, Arps, to refer to a new defence tactic in hostile mergers and acquisitions where differing takeover regimes in deals involving multi-jurisdictions are exploited to the advantage of a target company under threat.
Only from Spain did Louis XIV receive any good news where Das Minas and Galway had been forced to retreat from Madrid towards Valencia, allowing Philip V to re-enter his capital on 4 October.
From the 1930s to the 1960s, archaeologists like V. Gordon Childe and later John Hamilton regarded them as castles where local landowners held sway over a subject population.
Such syllables may be abbreviated CV, V, and CVC, where C stands for consonant and V stands for vowel.
Another place where a heterogeneous catalyst is applied is in the contact process ( oxidation of sulfur dioxide on vanadium ( V ) oxide for the production of sulfuric acid ).
A simple electric circuit, where current is represented by the letter i. The relationship between the voltage ( V ), resistance ( R ), and current ( I ) is V = IR ; this is known as Ohm's Law.
( V, T, P, S ), where N / V is the Non-terminal Variable, and Σ / T is the Terminal ) is context-sensitive if all rules in P are of the form
( Indeed, every production of a context free grammar is of the form V → w where V is a single nonterminal symbol, and w is a string of terminals and / or nonterminals ( w can be empty )).
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