Elements of matrix algebra

2022 ◽  
pp. 669-673
Keyword(s):  
Matrix Algebra

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

Matrix Algebra From a Statistician's Perspective

Technometrics ◽  
1998 ◽  
Vol 40 (2) ◽  
pp. 164-164 ◽  
Author(s):  
David A. Harville
Keyword(s):  
Matrix Algebra

scholarly journals The Center of the Quantized Matrix Algebra

1997 ◽  
Vol 196 (2) ◽  
pp. 458-474 ◽  
Author(s):  
Hans Plesner Jakobsen ◽  
Hechun Zhang
Keyword(s):  
Matrix Algebra

The Introduction of Matrix Algebra into Statistics

2006 ◽  
Vol 60 (2) ◽  
pp. 162-162 ◽  
Author(s):  
H. A David
Keyword(s):  
Matrix Algebra
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