Eigenvalue equalities for ordinary and Hadamard products of
... When A and B are real, the two sets of inequalities coniside. However, for complex A and B, as mentioned in [5, p.315], the eigenvalues of AB and AB T may not be the same and they provide different lower bounds in (5) and (6). In Section 5, using a result in Section 4, we determine their equality fo ...
... When A and B are real, the two sets of inequalities coniside. However, for complex A and B, as mentioned in [5, p.315], the eigenvalues of AB and AB T may not be the same and they provide different lower bounds in (5) and (6). In Section 5, using a result in Section 4, we determine their equality fo ...
The Coding Theory Workbook
... Two sets are said to be disjoint if they have no elements in common, i.e. X ∩ Y = ∅. ...
... Two sets are said to be disjoint if they have no elements in common, i.e. X ∩ Y = ∅. ...
Chapter One - Princeton University Press
... eigenvalues are nonnegative. A is strictly positive if and only if all its eigenvalues are positive. (ii) A is positive if and only if it is Hermitian and all its principal minors are nonnegative. A is strictly positive if and only if all its principal minors are positive. (iii) A is positive if and ...
... eigenvalues are nonnegative. A is strictly positive if and only if all its eigenvalues are positive. (ii) A is positive if and only if it is Hermitian and all its principal minors are nonnegative. A is strictly positive if and only if all its principal minors are positive. (iii) A is positive if and ...
An Interpretation of Rosenbrock`s Theorem Via Local
... Furthermore, all polynomial matrix representations also have the same left Wiener– Hopf factorization indices at infinity, which are equal to the controllability indices of (▭) and (▭), because the controllability indices are invariant under feedback. With all this in mind it is not hard to see that ...
... Furthermore, all polynomial matrix representations also have the same left Wiener– Hopf factorization indices at infinity, which are equal to the controllability indices of (▭) and (▭), because the controllability indices are invariant under feedback. With all this in mind it is not hard to see that ...
Some algebraic properties of differential operators
... (see e.g., Ref. 2) that any rational pseudodifferential operator R can be represented as a right (respectively, left) fraction AS − 1 (respectively, S1−1 A1 ), where A, A1 , S, S1 ∈ K[∂]. We show that these fractions have a unique representation in “lowest terms.” Namely, if S (respectively, S1 ) ha ...
... (see e.g., Ref. 2) that any rational pseudodifferential operator R can be represented as a right (respectively, left) fraction AS − 1 (respectively, S1−1 A1 ), where A, A1 , S, S1 ∈ K[∂]. We show that these fractions have a unique representation in “lowest terms.” Namely, if S (respectively, S1 ) ha ...
Notes on Blackwell`s Comparison of Experiments Tilman Börgers
... unchanged. Moreover, the expected value of a linear function equals the linear function evaluated at the expected value of the argument, and the expected values of ej and fk both equal the prior probability of state 1. Next, we note that the inequality remains true if we consider a finite linear com ...
... unchanged. Moreover, the expected value of a linear function equals the linear function evaluated at the expected value of the argument, and the expected values of ej and fk both equal the prior probability of state 1. Next, we note that the inequality remains true if we consider a finite linear com ...
Non-negative matrix factorization
NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.