The quaternionic determinant

By N. Cohen, S. Leo. 2000

81 citations recorded by the source corpus.

The determinant for complex matrices cannot be extended to quaternionic matrices. Instead, the Study determinant and the closely related q-determinant are widely used. We show that the Study determinant can be characterized as the unique functional which extends the absolute value of the complex determinant and discuss its spectral and linear algebraic aspects.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8258e678a7275b1552d29e614f75e14ab8e07f1a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Ivan Kyrchei
2. Graziano Gentili

In Geometry and Topology

1. Ivan Kyrchei
2. Graziano Gentili
3. Caterina Stoppato
4. Daniele C. Struppa
5. Irene Sabadini
6. Fabrizio Colombo
7. Riccardo Ghiloni
8. A. Perotti

In Statistical and Nonlinear Physics

1. Ivan Kyrchei
2. Graziano Gentili
3. Caterina Stoppato

Citations in the corpus

• Cramer's rule for quaternionic systems of linear equations (2008, methodology): “From [1,4] we obtain ddetA = Mdet(A∗ A) = SdetA = Ddet A, where SdetA and DdetA are the determinants of Study and of Dieudonné, respectively.”
• M\"obius transformations and the Poincar\'e distance in the quaternionic setting (2008, background): “Here we will present the main features of the determinant of 2 × 2 quaternionic matrices - giving simple, direct proofs of our assertions - for the sake of completeness (see also [7, 4]).”