Ad
related to: conjugate math symbol- Digital Games
Turn study time into an adventure
with fun challenges & characters.
- Printable Workbooks
Download & print 300+ workbooks
written & reviewed by teachers.
- Digital Games
Search results
Results from the WOW.Com Content Network
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}
The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. [3] It represents a specialized cursive type of the letter d , just as the integral sign originates as a specialized type of a long s (first used in print by ...
The conjugate transpose of a matrix with real entries reduces to the transpose of , as the conjugate of a real number is the number itself. The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2 × 2 {\displaystyle 2\times 2} real matrices, obeying matrix addition and multiplication:
A complex number is real if and only if it equals its own conjugate. The unary operation of taking the complex conjugate of a complex number cannot be expressed by applying only their basic operations addition, subtraction, multiplication and division. Argument φ and modulus r locate a point in the complex plane.
Conjugate transpose, the complex conjugate of the transpose of a matrix; Harmonic conjugate in complex analysis; Conjugate (graph theory), an alternative term for a line graph, i.e. a graph representing the edge adjacencies of another graph; In group theory, various notions are called conjugation: Inner automorphism, a type of conjugation ...
In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty relation corresponds to the symplectic form. Also, conjugate variables are related by Noether's theorem , which states that if the laws of physics are invariant with respect to a change in one of the conjugate variables, then the other conjugate ...
In mathematics, if G is a group and Π is a representation of it over the complex vector space V, then the complex conjugate representation Π is defined over the complex conjugate vector space V as follows: Π (g) is the conjugate of Π(g) for all g in G. Π is also a representation, as one may check explicitly.
A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary. Further, conjugate priors may give intuition by more transparently showing how a likelihood function updates a prior distribution.
Ad
related to: conjugate math symbol