particularly linear algebra, an orthonormal basis for an inner product space V {\displaystyle V} with finite dimension is a basis for V {\displaystyle V} whose...
15 KB (2,669 words) - 07:04, 1 September 2024
vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an...
9 KB (1,358 words) - 15:08, 13 October 2023
If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis. Any orthogonal basis can be used to define a system...
3 KB (529 words) - 08:09, 13 March 2024
Hilbert space (section Orthonormal bases)
coordinates with respect to an orthonormal basis, in analogy with Cartesian coordinates in classical geometry. When this basis is countably infinite, it allows...
128 KB (17,488 words) - 00:05, 24 September 2024
Orthogonal matrix (redirect from Orthonormal matrix)
algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is...
36 KB (4,802 words) - 16:45, 22 May 2024
linear combination of monomials. Sines and cosines form an (orthonormal) Schauder basis for square-integrable functions on a bounded domain. As a particular...
3 KB (336 words) - 02:35, 22 July 2022
by crossed diagonals. If (i, j, k) is a positively oriented orthonormal basis, the basis vectors satisfy the following equalities i × j = k j × k = i...
75 KB (11,475 words) - 18:39, 5 September 2024
Haar wavelet (redirect from Haar basis)
be represented in terms of an orthonormal basis. The Haar sequence is now recognised as the first known wavelet basis and is extensively used as a teaching...
27 KB (4,520 words) - 18:50, 29 July 2024
Inner product space (section Orthonormal sequences)
space has an orthonormal basis. The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis. The answer...
56 KB (7,305 words) - 10:53, 26 August 2024
Gram matrix (section Constructing an orthonormal basis)
{\displaystyle G} is also a normal matrix. The Gram matrix of any orthonormal basis is the identity matrix. Equivalently, the Gram matrix of the rows...
14 KB (2,683 words) - 17:04, 18 July 2024