AAS 03-190 Conformal Mapping among Orthogonal, Symmetric, and Skew-Symmetric Matrices
نویسنده
چکیده
This paper shows that Cayley Transforms, which map Orthogonal and SkewSymmetric matrices, may be considered the extension to matrix field of the complex conformal mapping function f1(z) = 1− z 1 + x . Then, by using a set of real matrices which are, simultaneously, Orthogonal and Symmetric (the Ortho−Sym matrices), it similarly shows how to extend two complex conformal mapping functions (namely, the f2(z) = i− z i + z , and the f3(z) = 1− z 1 + z i here called the clockwise, and the counter clockwise functions), to matrix field. This extension consists of some new one-to-one mapping relationships between Orthogonal and Symmetric, and between Symmetric and Skew-Symmetric matrices. This new relationships complete the picture of the one-to-one matrix mapping among Orthogonal, Symmetric, and SkewSymmetric matrices. Finally, this paper shows how to map among Orthogonal, Symmetric, and Skew-Symmetric matrices, by means of a direct product.
منابع مشابه
The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...
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