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...

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...

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...

coordinates with respect to an orthonormal basis, in analogy with Cartesian coordinates in classical geometry. When this basis is countably infinite, it allows...

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...

space has an orthonormal basis. The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis. The answer...

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...

linear combination of monomials. Sines and cosines form an (orthonormal) Schauder basis for square-integrable functions on a bounded domain. As a particular...

{\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...

norm, so that the rows constitute an orthonormal basis of V. The columns of the matrix form another orthonormal basis of V. If an orthogonal transformation...

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...

I}\|Ae_{i}\|_{H}^{2},} where { e i : i ∈ I } {\displaystyle \{e_{i}:i\in I\}} is an orthonormal basis. The index set I {\displaystyle I} need not be countable. However...

cost of an asset Basis function Basis (linear algebra) Dual basis Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating...

dimension n. Conversely, the choice of a point called the origin and an orthonormal basis of the space of translations is equivalent with defining an isomorphism...

when each element in B has norm 1, then B is an orthonormal basis of V. Let {bn} be a Schauder basis of a Banach space V over F = R or C. It is a subtle...

collectively the Frenet–Serret frame or TNB frame, together form an orthonormal basis spanning R 3 {\displaystyle \mathbb {R} ^{3}} and are defined as follows:...

other. By technical definition, it is a method of constructing an orthonormal basis from a set of vectors in an inner product space, most commonly the...

forms an orthonormal basis in the simplex. The values x i ∗ , i = 1 , 2 , … , D − 1 {\displaystyle x_{i}^{*},i=1,2,\ldots ,D-1} are the (orthonormal and Cartesian)...

columns of Q form an orthonormal basis for the column space of A. More generally, the first k columns of Q form an orthonormal basis for the span of the...

that is its own adjoint. If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is a Hermitian...

{\displaystyle U^{-1}=U^{*}} . The columns of U {\displaystyle U} form an orthonormal basis of C n {\displaystyle \mathbb {C} ^{n}} with respect to the usual...

I-P} can be computed by an orthonormal basis of A {\displaystyle A} . Let Q A {\displaystyle Q_{A}} be an orthonormal basis of A {\displaystyle A} and...

possible with classical mechanics. In addition, the Bell states form an orthonormal basis and can therefore be defined with an appropriate measurement. Because...

kernel of T admits either a finite orthonormal basis of eigenvectors of T, or a countably infinite orthonormal basis {en} of eigenvectors of T, with corresponding...

harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as...

= 1 ∞ {\displaystyle \left\{e_{n}\right\}_{n=1}^{\infty }} is an orthonormal basis for H {\displaystyle H} and U : H → H {\displaystyle U:H\rightarrow...

inner-product space. Let B {\displaystyle B} be an orthonormal basis of H {\displaystyle H} ; that is, an orthonormal set which is total in the sense that the linear...

An orthonormal function system (ONS) is an orthonormal basis in a vector space of functions. Melzak, Z. A. (2012), Companion to Concrete Mathematics,...

with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space of functions. This theory is important...

g, then an orthonormal frame at a point P of M is an ordered basis of the tangent space at P consisting of vectors which are orthonormal with respect...