Hello RG colleagues
I would like to ask you about the different ways of defining matrix powers that you may come in your areas of research, two common way to define powers of a matrix is through Cayley multiplication (approach restricted only to square matrices) and through element wise multiplication, based on Hadamard multiplication (approach applicable to both square and strictly rectangular matrices)
What other approaches of defining matrix powers, given the restriction that the matrix and its powers are elements of the same Matrix space, are you aware of/that you have used in computations, what are the salient features, if any, of this particular approach in your opinion ?
All opinions and comments are welcome.
Regards
D.Ghosh
I use Face-Splitting Product of matrices as well. More information you can find in these articles:
Article A family of face products of matrices and its properties
https://en.wikipedia.org/wiki/Khatri%E2%80%93Rao_product#Face-splitting_product
Preprint Almost Optimal Tensor Sketch
On the other hand, can be used Penetrating face product of matrices as an extension of Hadamard multiplication to block matrix:
https://en.wikipedia.org/wiki/Hadamard_product_(matrices)#The_penetrating_face_product
Article Generalized face-splitting matrix products in models of digi...
Thank you so very much Prof. Slyusar for the reply and cited references on face splitting matrix product, It is indeed a very interesting and revolutionary concept in area of matrix composition and I will get started on it to understand it in more details.
Regards
D.Ghosh
Thank you for your estimation. If you will have questions, you can ask me
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