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If the transition matrix of a Markov chain contains zero

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 2 Chapter 5.5

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Problem 2

If the transition matrix of a Markov chain contains zero emries. then it is not regular.

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Religion 372 Week 12 Notes **29.Mar.2016 (Thursday) - Week 12 Christianity in Ethiopia Sudan, Ethiopia, and Yemen are all places that have distinct Christian  traditions.  Christianity moves up and down the Red Sea  Ethiopia was known to the Romans before Christianity  Medieval Europeans knew of a place called Ethiopia and that it was Christian  Ethiopia was also a trading port as well. o Ethiopia is known!!  Frumentius o 300s ------------> 1959  Council of Chalcedon 451 "In 2 natures" o Roma and Constantinople accepts this. o Alexandria does not accept this Several Dynasties  Tegrey (4th-9th)  Lasta (9th-13th) - Zagwe  Shawa (13th-_) - Solomonic o All of these are Christin Dynasties the move farther and farther inland o Continuous Christian presence o Zagwe  Sometimes you get the churches that were built at Lalibela in this dynasty o Solomonic  Challenges the Zagwe dynasty on its origins and legitimacy, and the churches at Lalibela  Of the King of the Hebrews  Psalm 81:16  Has more of a Semitic kind of environment **31.Mar.2016 (Thursday) - Week 12 Kebra Nagast 14th century/ year 10-13  o In 14th century Ethiopia, what was going on culturally and politically o This is a political text.  Text from Ethiopia o Texts become part of a social world. o What goes into it/What comes out of it Religion 372 Week 13 Notes **05.Apr.2016 (Tuesday) - Week 13 Islam and Christianity  The apostolic tradition comes from Rome around the 3rd century  Before the time of Islam's expansion there were Christians in the general Middle East area  Plenty of Christians and Christian communities travelled along the Red Sea and placed themselves in the Western part of Saudi Arabia  Small Jewish populations as well o All kind of had to do with trade in some shape or way  Most of the Christians in the Red Sea/Arabian peninsula rejected the Council of Chalcedon - (431) - "in 2 natures."  Mecca o Cosmopolitan religion centre Christian Scriptures and the Qur'an  "Thou didst create of clay, as it were, the figure of a bird, by My leave, and didst breathe into it, and by My leave it became a bird."  Gospel of pseudo-Matthew, Ch.20  Surah {}  Surah 5:110 (left)  Infancy Gospel of Thomas, Ch.2 Expansion of Islam  Most of the areas that were taken over by practitioners of Islam were populated largely by Christians o Christian:  Monastic life  Thought  Belief  Practice o With these Christians, there were many that fell into different categories, not all agreed with each other and some were considered separatists o In North Africa, there were the Donatists, people that were in communion with Rome and other believers that were not.  Within 130 years or so the Muslims isolated the Roman churches, overtook the Greeks and the Syriac speaking areas that were populated by Christians  There was the loss of Jerusalem in this period of time  Questions that cropped up: o Why did God allow this to happen o Christians thought that they were the "chose people" so why are they being overtaken Pact of Omar  Follows fall of Jerusalem (636)  No new monasteries; church repair proscribed  Quiet worship only o No displaying crosses, processions, wooden clappers  No teaching Qur'an to Christian children  Taxation (dhimmi) especially for Christians  If you were part of the Persian Empire this kind of thing was not really new. Little changed for people who were already experiencing this/have already experienced it Perceptions of Islam  What if you were a Coptic Christian living in Egypt in the late 600s, what would your reaction to the expansion of Islam might have been  How might you have explained Islam's success theologically o Among other things, perhaps it was idolatry  John of Damascus: "Idolatry is not bad."  Islam was seen as Christianity gone awry. What is Islam Christian hereticism() Because we enjoy pictures on our religious buildings **07.Apr.2016 (Thursday) - Week 13 Class Cancelled Religion 372 Week 14 Notes **12.Apr.2016 (Tuesday) - Week 14 Patriarch Timothy's Dialogue (with the caliph)  One of the most interesting text from the first thousand years  Conversation between two sophisticated and highly intelligent elites  Highlights what Christianity is beginning to look like  How are Christians getting along in these Muslim empires How are they identifying themselves How do they talk about Islam and the Prophet Muhammad How do they position themselves o A time when Muslim empires were expanding On A Separate Note: Highlight from Tuesday The similarities and the contrasts about Christianity and Islam   On the level of practice things resemble one another  On the level of text there are things that overlap  Overlap in practices, people, literature/stories The Text  Timothy writes this, the caliph does not write the dialogue  It is strictly from the perspective of Timothy  This is copied and distributed to Christians which gives them the ammunition to defend their beliefs  The caliph moves the conversation along and allows Timothy to hit all of the points that he needs to focus on.  Timothy gives an intellectual tool to explain yourself.  On the Trinity: thinking of it as the sun: sun, light, and heat o Talking about the Christian language of begetting o The use of metaphorical language and talking about God. o The Son is eternally begotten of the Father in the Trinity  How metaphorical can you get with your language before it becomes nonsense  On Christ: o The two natures debate **14.Apr.2016 (Thursday) - Week 14 Christendom  It starts off as just a sect that is not distinctly separate and distinct and actually considered as other or another religion  Then people are being called heretics and anathematized leading Christians to go in in different directions and lead lives that they could grow into but still remaining Christian  "in" 2 natures and "of" 2 natures is what definitely separates Christians  Christianity (through Persians) made its way to China in the 600s o The Jesus Sutras o God being described as wind o Different ways to relate the religion to the Chinese way of life o Chinese converts are not borne fruitfully from this John from Rome makes it to China as an act of good will of European  Christians  Around the year 1,000 in Turkmenistan, in addition to all of the other "- stan" countries Christianity was an established religion and practice  Around the year 1,000 there are many introspective Christian communities in the East  In the Asia Minor region: o Christians -  Malkites  Jocobites  Nestorians o Political, Economic, and Educational Traffic is taking place in the geographical region in the Middle East/Central Asia  In the South: o Africa  Ethiopia  Miaphysites  The oneness of Jesus/God  The Orthodox World begins to push upwards because of the growing Islamic Empires in the east and the strong Latin Empires in the West  1054: o The Roman Catholic Church with the Pope in Rome and the Orthodox Church with the Patriarchates were friendly however in the year 1054 there was a split in between these two churches because of icons and idolatry  Philioque - the Holy Spirt proceeds from the Father and the Son [icons]  Dual Processionism  FATHER - SON - HOLY SPIRIT  Nicean Creed: Father  Holy Son Spirit o The Byzantine felt that they contained the holistic Christian world of Christendom true to its origins and Roma was like, "No, you are no longer the people who holds the truth of the tradition of Christianity. You are excommunicated."  In the first 300 years Christianity is truly a Mediterranean religion  Later on, the Frankish kingdom spread upward into Northern Europe  In the year 1,000 Iceland becomes a Christianized nation  Is there one version of Christianity or are there Christianities  The Son is fully Divine "You can sit with us."  In Agreement with Arius "You are heretical and forced out of communion and Christian tradition." o Then the Christian tradition must define itself as what it is not.  What is at the center What is Christianity oriented towards

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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

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If the transition matrix of a Markov chain contains zero