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Let be a orthogonal matrix given by (7).
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Given this drawback, constraining the kernel to be an orthogonal matrix may be a solution.
Here we use the fact |Λx| = |x| since Λ is a orthogonal matrix.
If,, where is an orthogonal matrix,,.
where K = K 1 K 2 ′ is an orthogonal matrix.
An (ntimes n) typical orthogonal matrix is an orthogonal matrix with one column equal to (pm u_{n}).
Let the spectral decomposition of be, where is an orthogonal matrix and Let, then (3.15).
Since V is an orthogonal matrix and A is symmetric positive definite, (V^{T}AV) is symmetric positive definite, too.
Since the R is an orthogonal matrix, the constrained optimization problem can be solved by the method of Lagrange multipliers.
It has been known that a square matrix can be triangularized by iterative QR transformations[26 28], where Q is an orthogonal matrix and R is an upper triangular matrix.
We note that is an orthogonal matrix which is similar to the one found in (12) for the conventional Alamouti scheme.
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