orthonormal basis sentence in Hindi
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- The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis.
- Every symmetric matrix is thus, up to choice of an orthonormal basis, a diagonal matrix.
- So is the kernel of the Fourier transform actually an orthonormal basis for L2 [ R ]?
- Applying the Gram Schmidt process to, there is a unique orthonormal basis and positive constants such that
- The rows of this matrix are mutually perpendicular unit vectors : an orthonormal basis of ! 3.
- Orthonormal basis vectors share the algebra of the Pauli matrices, but are usually not equated with them.
- Let be an orthonormal basis for, and let \ phi : F \ to B be a bijection.
- An orthonormal basis is a basis where all basis vectors have length 1 and are orthogonal to each other.
- Given any finite-dimensional vector space, an orthonormal basis could be found by the Gram Schmidt procedure.
- In this special case, the columns of are eigenvectors of both and and form an orthonormal basis in.
- The Hermite functions are thus an orthonormal basis of which " diagonalizes the Fourier transform operator ".
- The wedge products of elements of an orthonormal basis in form an orthonormal basis of the exterior algebra of.
- The wedge products of elements of an orthonormal basis in form an orthonormal basis of the exterior algebra of.
- One can complete the diagonalization of " T " by selecting an orthonormal basis of the kernel.
- This definition of orthonormal basis generalizes to the case of infinite-dimensional inner product spaces in the following way.
- If one chooses the eigenvectors of as an orthonormal basis, the matrix representation of in this basis is diagonal.
- If is a bounded domain in then the eigenfunctions of the Laplacian are an orthonormal basis for the Hilbert space.
- Note that an orthonormal basis in this sense is not generally a Hamel basis, since infinite linear combinations are required.
- Given a set of right-handed orthonormal basis vectors, the cross product is expressed in terms of its components as:
- In fact, in the presence of a positively oriented orthonormal basis, the exterior product generalizes these notions to higher dimensions.
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