Entropy of operator-valued random variables: A variational principle for large N matrix models
... models for random surfaces and M-theory (an approach to a string theory of quantum gravity). In all these theories, the observables are functions of the matrices which are invariant under changes of basis; in many cases — as for Yang–Mills theories — the invariance group is quite large since it cont ...
... models for random surfaces and M-theory (an approach to a string theory of quantum gravity). In all these theories, the observables are functions of the matrices which are invariant under changes of basis; in many cases — as for Yang–Mills theories — the invariance group is quite large since it cont ...
Linear Transformations and Matrix Algebra
... to θ via inverse trigonometric functions. These details will occur in |x||b| n chapter 6 where we find that by using the inner-product on vectors from R we will define the notion of angle and from that distance. Using these definitions and Schwarz’s inequality will then give us a triangle-inequality ...
... to θ via inverse trigonometric functions. These details will occur in |x||b| n chapter 6 where we find that by using the inner-product on vectors from R we will define the notion of angle and from that distance. Using these definitions and Schwarz’s inequality will then give us a triangle-inequality ...
An Applet-Based Proof of the Chebyshev Theorem
... A sectioned alternating set is an alternating set x0,...,xn-1 together with nontrivial closed intervals I0,...,In-1, called sections, with the following properties: • The intervals partition [a,b]. • For every i, xi is in Ii ...
... A sectioned alternating set is an alternating set x0,...,xn-1 together with nontrivial closed intervals I0,...,In-1, called sections, with the following properties: • The intervals partition [a,b]. • For every i, xi is in Ii ...
On a different kind of d -orthogonal polynomials that generalize the Laguerre polynomials
... The d-orthogonality notion seems to appear in various domains of mathematics. For instance, there is a closed relationship between 2-orthogonality and the birth and the death process [26]. Furthermore, Vinet and Zhedanov [24] showed that there exists a connection with application of d-orthogonal pol ...
... The d-orthogonality notion seems to appear in various domains of mathematics. For instance, there is a closed relationship between 2-orthogonality and the birth and the death process [26]. Furthermore, Vinet and Zhedanov [24] showed that there exists a connection with application of d-orthogonal pol ...