Misplaced Pages

This is an old revision of this page, as edited by Rxtreme (talk | contribs) at 21:27, 23 December 2018 (Added Hadamard gate (likely the most common use of Hadamard, related though not identical to the Hadamard matrix). Hadamard gate should really go to the section in the Quantum Logic Gates, though.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Hadamard may refer to:

• Jacques Hadamard (1865–1963), a French mathematician, whose name is associated with the following topics in mathematics:

Differential geometry

• Hadamard space, a geodesically complete metric space of non-positive curvature
• Cartan-Hadamard theorem, a result on the topology of non-positively curved manifolds

Differential equations and dynamical systems

• Hadamard's method of descent, a method of solving partial differential equations by reducing dimensions
• Hadamard parametrix construction, a method of solving second order partial differential equations
• Hadamard's dynamical system, a type of chaotic dynamical system

Complex analysis and convexity

• Hadamard three-lines theorem: a bound on the maximum modulus complex analytic functions defined on a strip in the complex plane;
• Hadamard three-circle theorem, a bound on the maximum modulus of complex analytic functions defined on an annulus in the complex plane; closely related to the three-lines theorem;
• Hadamard factorization theorem, a specific factorization of an entire function of finite order, involving its zeros and the exponential of a polynomial
• Ostrowski–Hadamard gap theorem, a result on the analytic continuation of lacunary power series
• Hermite–Hadamard inequality, bounding the integral of convex functions.

Transform calculus

• Hadamard transform, an example of a generalized class of Fourier transforms
• Fast Walsh–Hadamard transform, an efficient algorithm to compute the Hadamard transform

Theory of matrices

• Hadamard matrix, a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal
• Hadamard code, a system used for signal error detection and correction based on Hadamard matrices
• Hadamard's inequality, a bound on the determinants of matrices.

Quantum Computing

• Hadamard gate, a standard quantum gate that generalizes a coin flip.

• Disambiguation pages