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  2. Topological conjugacy - Wikipedia

    en.wikipedia.org/wiki/Topological_conjugacy

    In mathematics, two functions are said to be topologically conjugate if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy, and related-but-distinct § Topological equivalence of flows, are important in the study of iterated functions and more generally dynamical systems, since, if the dynamics of one iterative function can be determined, then that ...

  3. 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.

  4. Conjugation - Wikipedia

    en.wikipedia.org/wiki/Conjugation

    Conjugate (acid-base theory), a system describing a conjugate acid-base pair; Conjugated system, a system of atoms covalently bonded with alternating single and multiple bonds; Conjugate variables (thermodynamics), pairs of variables that always change simultaneously; Conjugate quantities, observables that are linked by the Heisenberg ...

  5. 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 ≡ ...

  6. Matrix similarity - Wikipedia

    en.wikipedia.org/wiki/Matrix_similarity

    In the definition of similarity, if the matrix P can be chosen to be a permutation matrix then A and B are permutation-similar; if P can be chosen to be a unitary matrix then A and B are unitarily equivalent. The spectral theorem says that every normal matrix is unitarily equivalent to some diagonal matrix.

  7. Conjugate variables - Wikipedia

    en.wikipedia.org/wiki/Conjugate_variables

    Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, [1] [2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle —between them.

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