<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-Orthogonal matrices

We say that A has a φ S polar decomposition if A = QT for some φ S orthogonal Q ∈ M n (C) and some φ S symmetric T ∈ M n (C). Let V S = {A ∈ M n (C) : φ S (φ S (A)) = A}. We show that every nonsingular A ∈ V S has a φ S polar decomposition. We determine conditions for which an A ∈ M n (C) has a φ S polar decomposition. We also determine the possible Jordan Canonical Forms of a φ S orthogonal matrix and of a φ S skew symmetric matrix.

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The ϕS polar decomposition

Granario

Merino

Paras

2013

Linear Algebra and its Applications

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Products of symplectic normal matrices

Cruz

Granario

2018

Linear Algebra and its Applications

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On the Lie algebra associated to S-unitary matrices

Caalim

Canlubo

Tanaka

2018

Linear Algebra and its Applications

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ϕS-Orthogonal matrices

Cited by 4 publications

References 7 publications

The ϕS polar decomposition

The ϕS polar decomposition

Products of symplectic normal matrices

On the Lie algebra associated to S-unitary matrices

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