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The conjugate spinor plays a role similar to that of θ < sup >*</ sup > in the superspace R < sup > 1 | 2 </ sup >, except that the Majorana condition, as manifested in the above equation, imposes that θ and θ < sup >*</ sup > are not independent.
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conjugate and spinor
We can also form a conjugate spinor
This Majorana spinor can be reexpressed as a complex left-handed Weyl spinor and its complex conjugate right-handed Weyl spinor ( they're not independent of each other ).
This superspace involves four extra fermionic coordinates, transforming as a two-component spinor and its conjugate.
Superspace contains the usual space-time coordinates,, and four extra fermionic coordinates, transforming as a two-component ( Weyl ) spinor and its conjugate.
This superspace involves four extra fermionic coordinates, transforming as a two-component spinor and its conjugate.
This superspace involves four extra fermionic coordinates, transforming as a two-component spinor and its conjugate.
In four dimensions, the simplest example — namely, the minimal N = 1 supersymmetry — may be written as a vector in a superspace with four extra fermionic coordinates, transforming as a two-component spinor and its conjugate.
conjugate and plays
If one thinks of operators on a Hilbert space as " generalized complex numbers ", then the adjoint of an operator plays the role of the complex conjugate of a complex number.
conjugate and role
In some sense, these operators play the role of the real numbers ( being equal to their own " complex conjugate ").
conjugate and similar
These conjugates Af had much less nonspecific staining than the previous conjugate ( with 50 mg FITC per gram of globulin ) while the specific staining was similar in both cases.
To put it in a slightly more complex way, similar to the concept of frequency and time used in traditional Fourier transform theory, Fourier optics makes use of the spatial frequency domain ( k < sub > x </ sub >, k < sub > y </ sub >) as the conjugate of the spatial ( x, y ) domain.
) Then the kernel is the space of multiples of exp ( λx ) if λ is an integral multiple of 2πi and is 0 otherwise, and the kernel of the adjoint is a similar space with λ replaced by its complex conjugate.
In the context of matrix groups, similarity is sometimes referred to as conjugacy, with similar matrices being conjugate.
When F is the field of complex numbers C, one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument.
Quaternionic representations are similar to real representations in that they are isomorphic to their complex conjugate representation.
If we are to show that X = AB ∩ DE, Y = BC ∩ EF, Z = CD ∩ FA are collinear for conconical ABCDEF, then notice that ADY and CYF are similar, and that X and Z will correspond to the isogonal conjugate if we overlap the similar triangles.
The conjugate satisfies similar properties to usual complex conjugate.
Any two splitting Cartan algebras are conjugate, and they fulfill a similar function to Cartan algebras in semisimple Lie algebras over algebraically closed fields, so split semisimple Lie algebras ( indeed, split reductive Lie algebras ) share many properties with semisimple Lie algebras over algebraically closed fields.
In this case, the pKa value of the agent is similar to the conjugate acid of the propagating carbanionic chain end.
conjugate and θ
This quantity J is canonically conjugate to a variable θ which, by the Hamilton equations of motion changes with time as the gradient of energy with J.
The final expression is clarified by introducing the variable canonically conjugate to J, which is called the angle variable θ.
can be expressed as cos θ for an angle θ ; in geometric terms there are two eigenvalues accounting for the remainder and with the denominator as given they are complex conjugate and of absolute value 1.
In Bayesian probability theory, if the posterior distributions p ( θ | x ) are in the same family as the prior probability distribution p ( θ ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood.
conjugate and <
Reactions of acids are often generalized in the form HA H < sup >+</ sup > + A < sup >−</ sup >, where HA represents the acid and A < sup >−</ sup > is the conjugate base.
Note that the acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA < sup >+</ sup > H < sup >+</ sup > + A.
The numerical value of K < sub > a </ sub > is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid ( HA ) and the products are the conjugate base and H < sup >+</ sup >.
where n < sup > c </ sup > denotes the charge conjugate state, i. e., the antiparticle.
Amide can also refer to the conjugate base of ammonia ( the anion H < sub > 2 </ sub > N < sup >–</ sup >) or of an organic amine ( an anion R < sub > 2 </ sub > N < sup >–</ sup >).
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.
If A is expressed as an N × N matrix, then A < sup >†</ sup > is its conjugate transpose.
In what follows, c < sub > 1 </ sub > and c < sub > 2 </ sub > denote arbitrary complex numbers, c * denotes the complex conjugate of c, A and B denote arbitrary linear operators, and these properties are to hold for any choice of bras and kets.
It is the conjugate base of the hydrogen carbonate ( bicarbonate ) ion, HCO < sub > 3 </ sub >< sup >−</ sup >, which is the conjugate base of H < sub > 2 </ sub > CO < sub > 3 </ sub >, carbonic acid.
The expression a < sup > x </ sup > denotes the conjugate of a by x, defined as x < sup >− 1 </ sup > a x.
Many other group theorists define the conjugate of a by x as xax < sup >− 1 </ sup >.
conjugate and >*</
: where M is any Hermitian positive-definite matrix, and x < sup >*</ sup > the conjugate transpose of x.
rk ( A < sup >*</ sup >), where A < sup >*</ sup > is the conjugate transpose or hermitian transpose of A.
where γ < sup >*</ sup > is the conjugate of γ, and the product is Clifford multiplication.
More generally, an complex matrix M is said to be positive definite if z < sup >*</ sup > Mz is real and positive for all non-zero complex vectors z ; where z < sup >*</ sup > denotes the conjugate transpose of z.
Therefore, the system is invariant under transformations of the ψ field and its complex conjugate field ψ < sup >*</ sup > that leave | ψ |< sup > 2 </ sup > unchanged, such as
The conjugate transpose of the complex matrix A, written as A < sup >*</ sup >, is obtained by taking the transpose of A and the complex conjugate of each entry:
where M < sup >*</ sup > denotes the conjugate transpose of M. Other authors retain the definition () for complex matrices and call matrices satisfying () conjugate symplectic.
The conjugate ( a, b )< sup >*</ sup > of ( a, b ) is given by
The antiquark field belongs to the complex conjugate representation ( 3 < sup >*</ sup >) and also contains a triplet of fields.
In mathematics, the conjugate transpose, Hermitian transpose, Hermitian conjugate, or adjoint matrix of an m-by-n matrix A with complex entries is the n-by-m matrix A < sup >*</ sup > obtained from A by taking the transpose and then taking the complex conjugate of each entry ( i. e., negating their imaginary parts but not their real parts ).
The conjugate transpose " adjoint " matrix A < sup >*</ sup > should not be confused with the adjugate adj ( A ), which is also sometimes called " adjoint ".
Here r < sup >*</ sup > refers to the complex conjugate of r.
If we specifically choose the Euclidean norm on both R < sup > n </ sup > and R < sup > m </ sup >, then we obtain the matrix norm which to a given matrix A assigns the square root of the largest eigenvalue of the matrix A < sup >*</ sup > A ( where A < sup >*</ sup > denotes the conjugate transpose of A ).
Another generalization defines a complex Hadamard matrix to be a matrix in which the entries are complex numbers of unit modulus and which satisfies H H < sup >*</ sup >= n I < sub > n </ sub > where H < sup >*</ sup > is the conjugate transpose of H. Complex Hadamard matrices arise in the study of operator algebras and the theory of quantum computation.
with χ a primitive Dirichlet character, χ < sup >*</ sup > its complex conjugate, Λ the L-function multiplied by a gamma-factor, and ε a complex number of absolute value 1, of shape
0.282 seconds.