Rajendra Bhatia, Kalyan K. Mukherjea
Abstract
Abstract Let f 1 , ⃛, f n be a basis of unit vectors and g 1 , ⃛, g n an orthonormal basis in a Hilbert space. We consider and solve the problem of finding an orthonormal basis e 1 , ⃛, e n such that a weighted average of the distance of e j from f j and g j is minimized in the sense of least squares.
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Abstract Let f 1 , ⃛, f n be a basis of unit vectors and g 1 , ⃛, g n an orthonormal basis in a Hilbert space. We consider and solve the problem of finding an orthonormal basis e 1 , ⃛, e n such that a weighted average of the distance of e j from f j and g j is minimized in the sense of least squares.
Key concepts: Orthogonalization, Orthonormal basis, Basis (linear algebra), Hilbert space, Mathematics, Orthogonality, Orthonormality, Orthogonal basis