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  2. Conjugacy class - Wikipedia

    en.wikipedia.org/wiki/Conjugacy_class

    Two elements , are conjugate if there exists an element such that =, in which case is called a conjugate of and is called a conjugate of . In the case of the general linear group GL ⁡ ( n ) {\displaystyle \operatorname {GL} (n)} of invertible matrices , the conjugacy relation is called matrix similarity .

  3. Complex conjugate - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate

    Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane.The complex conjugate is found by reflecting across the real axis.. 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.

  4. Conjugate (acid-base theory) - Wikipedia

    en.wikipedia.org/wiki/Conjugate_(acid-base_theory)

    One use of conjugate acids and bases lies in buffering systems, which include a buffer solution. In a buffer, a weak acid and its conjugate base (in the form of a salt), or a weak base and its conjugate acid, are used in order to limit the pH change during a titration process. Buffers have both organic and non-organic chemical applications.

  5. Conjugated system - Wikipedia

    en.wikipedia.org/wiki/Conjugated_system

    Cinnamaldehyde is a naturally-occurring compound that has a conjugated system penta-1,3-diene is a molecule with a conjugated system Diazomethane conjugated pi-system. In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability.

  6. Acid dissociation constant - Wikipedia

    en.wikipedia.org/wiki/Acid_dissociation_constant

    In solution chemistry, it is common to use H + as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution H + denotes a solvated hydronium ion rather than a proton. [9] [10] The designation of an acid or base as "conjugate" depends on the context. The conjugate acid BH + of a base B dissociates according to

  7. Character table - Wikipedia

    en.wikipedia.org/wiki/Character_table

    The irreducible complex characters of a finite group form a character table which encodes much useful information about the group G in a concise form. Each row is labelled by an irreducible character and the entries in the row are the values of that character on any representative of the respective conjugacy class of G (because characters are class functions).

  8. Bra–ket notation - Wikipedia

    en.wikipedia.org/wiki/Bra–ket_notation

    The Hermitian conjugate of the Hermitian conjugate of anything (linear operators, bras, kets, numbers) is itself—i.e., (†) † =. Given any combination of complex numbers, bras, kets, inner products, outer products, and/or linear operators, written in bra–ket notation, its Hermitian conjugate can be computed by reversing the order of the ...

  9. Conjugate transpose - Wikipedia

    en.wikipedia.org/wiki/Conjugate_transpose

    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 + i b ≡ ...