Only addition is used when calculating the matrix-vector product of \ mathrm { A } and \ mathrm { L \ Pi f }.
12.
Iterative methods, such as conjugate gradient method and GMRES utilize fast computations of matrix-vector products Ax _ i, where matrix A is sparse.
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*PM : vector product in general vector spaces, id = 6089-- WP guess : vector product in general vector spaces-- Status:
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*PM : vector product in general vector spaces, id = 6089-- WP guess : vector product in general vector spaces-- Status:
15.
Validity is retained if & phi; is a vector, in which case the vector-vector product in the second term will be a dyad.
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For a given u \ in \ mathbb { R } ^ n, this method efficiently calculates the Hessian-vector product H ( x ) u.
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Let t be a tensor, b a basis and M a matrix for relating a new basis to b by expressing it as the matrix-vector product Mb.
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I tried solving it with a Matrix equation, and the vector would be the transpose of x is the vector product if the matrix equation is Ax = 0.
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Note that the products lacking dots are tensor products of tensors with vectors ( resulting in vectors similar to a matrix-vector product ), those with dots are dot products.
20.
This is easy to check for e . g . vectors, and as everything in the algebra can be built from vector products it applies to all elements of the algebra.
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