Skew symmetric matrices generate orthogonal matrices with determinant 1 through the exponential map.
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3x3 skew symmetric matrices can be used to represent cross products as matrix multiplications.
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This form also makes visible that the skew symmetric operator introduces error when the velocity field diverges.
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A newer version of MSTG, in which the skew symmetric tensor field was replaced by a vector field, is scalar tensor vector gravity ( STVG ).
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The general symplectic group GSp 2 " n " ( " R " ) consists of the automorphisms of a module multiplying a skew symmetric form by some invertible scalar.
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"' Note on the minus sign "': By using the skew symmetric matrix of position vectors relative to the reference point, the inertia matrix of each particle has the form " " m " [ r ] 2, which is similar to the " mr " 2 that appears in planar movement.
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If the abelian variety has a principal polarization then the form on ( is skew symmetric which implies that the order of ( is a square or twice a square ( if it is finite ), and if in addition the principal polarization comes from a rational divisor ( as is the case for elliptic curves ) then the form is alternating and the order of ( is a square ( if it is finite ).
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