### Some articles on *orthonormal*:

**Orthonormal**Function System

... An

**orthonormal**function system (ONS) is an

**orthonormal**basis in a vector space of functions ...

Bessel's Inequality

... is a statement about the coefficients of an element in a Hilbert space with respect to an

... is a statement about the coefficients of an element in a Hilbert space with respect to an

**orthonormal**sequence ... Let be a Hilbert space, and suppose that is an**orthonormal**sequence in ... For a complete**orthonormal**sequence (that is, for an**orthonormal**sequence which is a basis), we have Parseval's identity, which replaces the ...Wavelet Transform - Formal Definition

... A function is called an

... A function is called an

**orthonormal**wavelet if it can be used to define a Hilbert basis, that is a complete**orthonormal**system, for the Hilbert space of square integrable functions ... This family is an**orthonormal**system if it is**orthonormal**under the inner product where is the Kronecker delta and is the standard inner product on The requirement of ... This implies that an**orthonormal**wavelet is self-dual ...Theorems And Definitions In Linear Algebra - Inner Product Spaces - Properties of

... Suppose that is an

**Orthonormal**Set... Suppose that is an

**orthonormal**set in an -dimensional inner product space V ... Than (a) S can be extended to an**orthonormal**basis for V ...Compact Operator On Hilbert Space - Compact Self Adjoint Operator - Spectral Theorem

... every compact self-adjoint operator T on a real or complex Hilbert space H, there exists an

... every compact self-adjoint operator T on a real or complex Hilbert space H, there exists an

**orthonormal**basis of H consisting of eigenvectors of T ... of the 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 eigenvalues {λn ... one can mix the basis {en} with a countable**orthonormal**basis for the kernel of T, and obtain an**orthonormal**basis {fn} for H, consisting of eigenvectors of T with real eigenvalues {μn} such that μn → 0 ...Main Site Subjects

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