The spectral theorem in quaternions

By Douglas R. Farenick, Barbara A.F. Pidkowich. 2003

159 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d2857f577cd176669d86a0896955158428293eaa

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Entire slice regular functions (2015, background): “The case of quaternionic normal matrices was proved in [89] and it is based on the right spectrum, but the right spectrum is equal to the S-spectrum in the finite dimensional case.”
The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum (2014, unknown): “f a linear operator, the point S-spectrum coincides with the set of right eigenvalues. In the literature the spectral theorem for quaternionic normal matrices based on the right spectrum is proved in [21]. In the literature, there are some papers on the quaternionic spectral theorem, see, e.g., [22,”
The Spectral Theorem for Unitary Operators Based on the S-Spectrum (2014, unknown): “[22], [31], [32], however, except for the finite dimensional case in which the notion of spectrum is associated to an eigenvalue problem, see [21], it is not specified which notion of spectrum underlies the theorem.”
Ranks and the least-norm of the general solution to a system of quaternion matrix equations (2009, unknown): “We first simplify the definition of quaternionic inner product space defined in [20] as follows: A right H-vector space V is a quaternionic inner product space if there is a function (·, ·): V × V → H such that for all q1, q2 ∈ H and ζ, ζ1, ζ2 ∈ V : (1) (ζ1q1 + ζ2q2, ζ ) = q1(ζ1, ζ ) + q2(ζ2, ζ ); (”
On the eigenvalues of quaternion matrices (2011, unknown): “3 of [9].”
Geršgorin type theorems for quaternionic matrices (2007, background): “The theory on right eigenvalues of quaternionic matrices has been well established [8,16,17,26], while little is known for left eigenvalues.”
On solutions to the quaternion matrix equation AXB+CYD=E (2008, unknown): “Motivated by the work mentioned above, and keeping the applications and interests of quaternion matrices in view (e.g., [1], [ 3 ], [25]-[32], [36]-[37]), in this paper we consider the real and pure imaginary solutions to (1.4) over H .W e f irst derive the formulas for extremal ranks of real matric”