Pédagogie > BOYLE MIKE
http://indexation.univ-fcomte.fr/ori-oai-search/
Mon, 09 Sep 2024 21:15:04 GMTMike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 4)Mon, 24 Jun 2013 22:00:00 GMTLecture
I. I’ll give a complete elementary presentation of the essential
features of the Perron Frobenius theory of nonnegative matrices for the
central case of primitive matrices (the "Perron" part). (The "Frobenius"
part, for irreducible matrices, and finally the case for general
nonnegative matrices, will be described, with proofs left to
accompanying notes.) For integer matrices we’ll relate "Perron numbers"
to this and Mahler measures. Lecture II. I’ll describe how the
Perron-Frobenius theory generalizes (and fails to generalize) to 1,2,... x 1,2,...
nonnegative matrices. Lecture III. We’ll see the simple, potent
formalism by which a certain zeta function can be associated to a
nonnegative matrix, and its relation to the nonzero spectrum of the
matrix, and how polynomial matrices can be used in this setting for
constructions and conciseness. Lecture IV. We’ll describe a natural
algebraic equivalence relation on finite square matrices over a semiring
(such as Z, Z_+, R, ... ) which refines the nonzero spectrum and is
related to K-theory.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22721
oai:canal-u.fr:22721URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22721 ]]>Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 2)Thu, 20 Jun 2013 22:00:00 GMTLecture
I. I’ll give a complete elementary presentation of the essential
features of the Perron Frobenius theory of nonnegative matrices for the
central case of primitive matrices (the "Perron" part). (The "Frobenius"
part, for irreducible matrices, and finally the case for general
nonnegative matrices, will be described, with proofs left to
accompanying notes.) For integer matrices we’ll relate "Perron numbers"
to this and Mahler measures. Lecture II. I’ll describe how the
Perron-Frobenius theory generalizes (and fails to generalize) to 1,2,... x 1,2,...
nonnegative matrices. Lecture III. We’ll see the simple, potent
formalism by which a certain zeta function can be associated to a
nonnegative matrix, and its relation to the nonzero spectrum of the
matrix, and how polynomial matrices can be used in this setting for
constructions and conciseness. Lecture IV. We’ll describe a natural
algebraic equivalence relation on finite square matrices over a semiring
(such as Z, Z_+, R, ... ) which refines the nonzero spectrum and is
related to K-theory.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22711
oai:canal-u.fr:22711URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22711 ]]>Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 1)Mon, 17 Jun 2013 22:00:00 GMTLecture
I. I’ll give a complete elementary presentation of the essential
features of the Perron Frobenius theory of nonnegative matrices for the
central case of primitive matrices (the "Perron" part). (The "Frobenius"
part, for irreducible matrices, and finally the case for general
nonnegative matrices, will be described, with proofs left to
accompanying notes.) For integer matrices we’ll relate "Perron numbers"
to this and Mahler measures. Lecture II. I’ll describe how the
Perron-Frobenius theory generalizes (and fails to generalize) to 1,2,... x 1,2,...
nonnegative matrices. Lecture III. We’ll see the simple, potent
formalism by which a certain zeta function can be associated to a
nonnegative matrix, and its relation to the nonzero spectrum of the
matrix, and how polynomial matrices can be used in this setting for
constructions and conciseness. Lecture IV. We’ll describe a natural
algebraic equivalence relation on finite square matrices over a semiring
(such as Z, Z_+, R, ... ) which refines the nonzero spectrum and is
related to K-theory.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22709
oai:canal-u.fr:22709URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22709 ]]>