orthonormal's Usage Examples:

linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are.

product space are orthonormal if they are orthogonal (or perpendicular along a line) unit vectors.

A set of vectors form an orthonormal set if all vectors.

function by a certain orthonormal series generated by a wavelet.

This article provides a formal, mathematical definition of an orthonormal wavelet and of the.

algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors.

, en} is orthonormal if ⟨ei, ej⟩ = 0 for every i ≠ j and ⟨ei, ei⟩ = ||ei|| = 1 for each i.

This definition of orthonormal basis generalizes to.

the first two conditions basis is called an orthonormal system or an orthonormal set (or an orthonormal sequence if B is countable).

possible to talk about the set of all of orthonormal frames for Ex.

An orthonormal frame for Ex is an ordered orthonormal basis for Ex, or, equivalently, a linear.

In particular, orthogonal transformations map orthonormal bases to orthonormal bases.

Usually the sequence is required to be orthonormal, namely, ⟨ P n , P n ⟩ = 1 , {\displaystyle \langle P_{n},P_{n}\rangle.

is the norm of H, { e i : i ∈ I } {\displaystyle \{e_{i}:i\in I\}} an orthonormal basis of H.

is an orthonormal basis.

Orthogonal (not necessarily orthonormal) bases.

\|x\|^{2}} , where the equality holds if and only if S is an orthonormal basis; i.

, maximal orthonormal set.

an element x {\displaystyle x} in a Hilbert space with respect to an orthonormal sequence.

If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is self-adjoint if and only.

, Um of U yield an orthonormal basis of Km and the columns V1, .

, Vn of V yield an orthonormal basis of Kn (with respect to the standard.

field (also called a tetrad or vierbein) is a set of four pointwise-orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian.

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

matrix coefficients of the irreducible unitary representations form an orthonormal basis of L2(G).

An orthonormal function system (ONS) is an orthonormal basis in a vector space of functions.