21. The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis . 22. Every symmetric matrix is thus, up to choice of an orthonormal basis , a diagonal matrix. 23. So is the kernel of the Fourier transform actually an orthonormal basis for L2 [ R ]? 24. Applying the Gram Schmidt process to, there is a unique orthonormal basis and positive constants such that 25. The rows of this matrix are mutually perpendicular unit vectors : an orthonormal basis of ! 3. 26. Orthonormal basis vectors share the algebra of the Pauli matrices, but are usually not equated with them.27. Let be an orthonormal basis for, and let \ phi : F \ to B be a bijection. 28. An orthonormal basis is a basis where all basis vectors have length 1 and are orthogonal to each other. 29. Given any finite-dimensional vector space, an orthonormal basis could be found by the Gram Schmidt procedure. 30. In this special case, the columns of are eigenvectors of both and and form an orthonormal basis in.
