# skew-symmetric matrix

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Related to skew-symmetric matrix: Orthogonal matrix

## skew-symmetric matrix

[′skyü si¦me·trik ′mā·triks]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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For a three-order square matrix A, it is easy to see that (A - [A.sup.T]) is a skew-symmetric matrix. Denoting
As W is a skew-symmetric matrix and [eta] < 0 is a real number, then -[eta]([x.sup.*]Wx/[x.sup.*]x) is a pure imaginary.
Substituting (10)-(12) into (18) and using the property of skew-symmetric matrix [[omega].sup.x], it follows that
with respect to a pseudo-orthonormal frame {O; [u.sub.1], [u.sub.2],..., [u.sub.2n+1]}, whose A is the normal formed skew-symmetric matrix and C is a (2n + 1) x 1 column matrix such that
Further, if A is a skew-symmetric matrix, then we write [A.sub.I] for [A.sup.I.sub.I] in short.
Let L [member of] [L.sub.m]([C.sup.n x n]) be a complex symmetric or complex skew-symmetric matrix polynomial of the form (1.1).
Zhou, Solutions of matrix equation AX[A.sup.T] = C in symmetric and skew-symmetric matrix set (In Chinese), J.
where [[??].sub.3] is a skew-symmetric matrix associated to the unit vector [[??].sub.3] directed to the positive direction of [z.sub.k] axis.
where S is a skew-symmetric matrix. Such an implementation of GMRES is storage-free, a desirable feature in an iterative solver.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a skew-symmetric matrix associated to the unit vector [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
As the gyroscopic matrix G is missing, we choose a randomly generated skew-symmetric matrix with the same sparsity pattern as K and with entries of considerably smaller magnitude as the influence of the Coriolis force is usually much smaller than that of the stiffness of the system.

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