<?xml version="1.0" encoding="UTF-8"?><metadata>
<lom xmlns="http://ltsc.ieee.org/xsd/LOM" xmlns:lomfr="http://www.lom-fr.fr/xsd/LOMFR" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://ltsc.ieee.org/xsd/LOM http://www.lom-fr.fr/xsd/lomfrv1.0/std/lomfr.xsd">
<general>
    <identifier>
        <catalog>Canal-U_Ocms</catalog>
        <entry>22711</entry>
    </identifier>
    <title><string language="fre"><![CDATA[Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 2)]]></string></title>
    <language>ENG</language>
    <description>
        <string language="fre"><![CDATA[Lecture
 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.]]></string></description>
    <keyword><string language="fre"><![CDATA[mathématiques]]></string></keyword><keyword><string language="fre"><![CDATA[Grenoble]]></string></keyword><keyword><string language="fre"><![CDATA[école d'été]]></string></keyword><keyword><string language="fre"><![CDATA[dynamics]]></string></keyword><keyword><string language="fre"><![CDATA[institut fourier]]></string></keyword><keyword><string language="fre"><![CDATA[summer school]]></string></keyword><keyword><string language="fre"><![CDATA[number theory]]></string></keyword>
    <lomfr:documentType>
        <lomfr:source>LOMFRv1.0</lomfr:source>
        <lomfr:value>image en mouvement</lomfr:value>
    </lomfr:documentType>
</general><lifeCycle>
    
    <contribute>
            <role>
                <source>LOMv1.0</source>
                <value>author</value>
            </role>
            <entity><![CDATA[BEGIN:VCARD
VERSION:3.0
CLASS:PUBLIC
REV:2016-06-19 00:01:05
FN:Mike Boyle
N:Boyle;Mike;;;

URL;TYPE=work:http://www.math.umd.edu/~mboyle/
ROLE:author
TZ:+0200
END:VCARD
]]></entity>
            <date><dateTime>2013-06-21</dateTime></date>
        </contribute>

    <contribute>
            <role>
                <source>LOMv1.0</source>
                <value>content provider</value>
            </role>
            <entity><![CDATA[BEGIN:VCARD
VERSION:3.0
CLASS:PUBLIC
REV:2016-06-19 00:01:05
FN:Fanny Bastien
N:Bastien;Fanny;;;

URL;TYPE=work:http://www.canal-u.tv/auteurs/bastien_fanny
ROLE:content provider
TZ:+0200
END:VCARD
]]></entity>
            <date><dateTime>2013-06-21</dateTime></date>
        </contribute>

</lifeCycle>
<metaMetadata>
    <metadataSchema>LOMv1.0</metadataSchema>
    <metadataSchema>LOMFRv1.0</metadataSchema>
</metaMetadata>
<technical>
    <format>video/x-flv</format>
    <location><![CDATA[http://www.canal-u.tv/video/institut_fourier/mike_boyle_nonnegative_matrices_perron_frobenius_theory_and_related_algebra_part_2.22711]]></location>
    <location><![CDATA[rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/mike.boyle.nonnegative.matrices.perron.frobenius.theory.and.related.algebra.part.2._22711/boyle_ecoleete_21062013_sd.mp4]]></location>
        
        
    <size>2953879567</size>
    <duration><duration>PT1H15M53S</duration></duration>
</technical>
<educational>
    <learningResourceType>
        <source>LOMv1.0</source>
        <value>lecture</value>
    </learningResourceType>
    
    <context>
        <source>LOMv1.0</source>
        <value>doctorat</value>
    </context>
</educational>
<rights>
    <cost>
        <source>LOMv1.0</source>
        <value>no</value>
    </cost>
    <copyrightAndOtherRestrictions>
        <source>LOMv1.0</source>
        <value>no</value>
    </copyrightAndOtherRestrictions>
    <description>
        <string language="fre"><![CDATA[Droits réservés à l'éditeur et aux auteurs. 
CC BY-NC-ND 4.0]]></string>
    </description>
</rights>

            <relation>
                <kind>
                    <source>LOMv1.0</source>
                    <value>ispartof</value>
                </kind>
                <resource>
                    <identifier>
                        <catalog>URI</catalog>
                        <entry>http://www.canal-u.tv/producteurs/institut_fourier/ecoles_d_ete</entry>
                    </identifier>
                    <description>
                        <string language="fre"><![CDATA[Ecoles d'été]]></string>
                    </description>
                </resource>
            </relation>

            <relation>
                <kind>
                    <source>LOMv1.0</source>
                    <value>ispartof</value>
                </kind>
                <resource>
                    <identifier>
                        <catalog>URI</catalog>
                        <entry>http://www.canal-u.tv/producteurs/institut_fourier/ecoles_d_ete</entry>
                    </identifier>
                    <description>
                        <string language="fre"><![CDATA[2013]]></string>
                    </description>
                </resource>
            </relation>

<classification>
    <purpose>
        <source>LOMv1.0</source>
        <value>discipline</value>
    </purpose>
    <taxonPath>
        <source>
        <string language="fre"><![CDATA[Universités Numériques Thématiques 2009 http://www.universites-numeriques.fr]]></string>
        </source>
        <taxon>
            <id/>
            <entry>
                <string language="fre"/>
            </entry>
        </taxon>
    </taxonPath>
</classification>
<classification>
    <purpose>
        <source>LOMv1.0</source>
        <value>discipline</value>
    </purpose>
    
    <taxonPath>
        <source>
            <string language="fre">CDD 22e éd.</string>
            <string language="eng">DDC 22nd ed.</string>
        </source>
        <taxon>
            <id>510</id>
            <entry>
                <string language="fre"><![CDATA[Mathématiques]]></string>
            </entry>
        </taxon>
   </taxonPath>
</classification>      </lom>
   </metadata>