On Elementary Unitary and Φ-unitary Transformations
نویسنده
چکیده
We introduce a simple uniform structure of elementary Φ-unitary matrices. Elementary Φ-unitary transformations are the extentions of Householder transformations in real and complex spaces with a definite or an indefinite inner product induced by a nonsingular signature matrix Φ. The extentions are found useful in the computations of complex matrices or special structured matrices. For two (complex) vectors a and b, we present the sufficient and necessary conditions on the existence of an elementary Φ-unitary transformation U such that Ua = b. And we discuss some impacts of the theory on matrix computations involving Φ-unitary transformations.
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