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Mixed matrix pencils: Nonstandard involutions
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This chapter also studies the canonical forms of mixed quaternion matrix pencils, i.e., such that one of the two matrices is φ-hermitian and the other is φ-skewhermitian, with respect to simultaneous φ-congruence. It starts by formulating the canonical form for φ-hsk matrix pencils under strict equivalence. Other canonical forms of mixed matrix pencils are developed with respect to strict equivalence. As an application, this chapter provides canonical forms of quaternion matrices under φ-congruence. As in the preceding chapter, this chapter also fixes a nonstandard involution φ throughout and a quaternion β(φ) such that φ=(β(φ)) = −β(φ) and ∣β(φ)∣ = 1.
Title: Mixed matrix pencils: Nonstandard involutions
Description:
This chapter also studies the canonical forms of mixed quaternion matrix pencils, i.
e.
, such that one of the two matrices is φ-hermitian and the other is φ-skewhermitian, with respect to simultaneous φ-congruence.
It starts by formulating the canonical form for φ-hsk matrix pencils under strict equivalence.
Other canonical forms of mixed matrix pencils are developed with respect to strict equivalence.
As an application, this chapter provides canonical forms of quaternion matrices under φ-congruence.
As in the preceding chapter, this chapter also fixes a nonstandard involution φ throughout and a quaternion β(φ) such that φ=(β(φ)) = −β(φ) and ∣β(φ)∣ = 1.
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