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Unformatted text preview: Linear Algebra Math1111 What’s the use of Linear Algebra? Example  An Economic Model Example . People in an ancient tribe have three occupations: farming (F), maunfacturing tools (M) & sewing clothes(C). Farmers keep some of their products and give maunfacturers some to exchange tools, etc. F M C F 1 2 1 3 1 2 M 1 4 1 3 1 4 C 1 4 1 3 1 4 People in the tribe want to introduce a monetary system. Linear Algebra Math1111 What’s the use of Linear Algebra? Example  An Economic Model Example . People in an ancient tribe have three occupations: farming (F), maunfacturing tools (M) & sewing clothes(C). Farmers keep some of their products and give maunfacturers some to exchange tools, etc. F M C F 1 2 1 3 1 2 M 1 4 1 3 1 4 C 1 4 1 3 1 4 People in the tribe want to introduce a monetary system. Question. How to value their products ? Linear Algebra Math1111 What’s the use of Linear Algebra? Example  An Economic Model Example . People in an ancient tribe have three occupations: farming (F), maunfacturing tools (M) & sewing clothes(C). Farmers keep some of their products and give maunfacturers some to exchange tools, etc. F M C F 1 2 1 3 1 2 M 1 4 1 3 1 4 C 1 4 1 3 1 4 People in the tribe want to introduce a monetary system. Question. How to value their products ? This is an example of the closed Leontief inputoutput model, developed by the Nobel prize winning economist Wassily Leontief. Linear Algebra Math1111 What’s the use of Linear Algebra? Example  Google Google  a search engine • Input a keyword, then Google outputs a list of relevant websites ranked by popularity or importance . Linear Algebra Math1111 What’s the use of Linear Algebra? Example  Google Google  a search engine • Input a keyword, then Google outputs a list of relevant websites ranked by popularity or importance . How to weight importance ? • Impose suitable assumptions and collect data. Linear Algebra Math1111 What’s the use of Linear Algebra? Example  Google Google  a search engine • Input a keyword, then Google outputs a list of relevant websites ranked by popularity or importance . How to weight importance ? • Impose suitable assumptions and collect data. How to handle the data? A method is conceived by two Standford graduate students: Sergey Brin & Larry Page (both born in 1973) Linear Algebra Math1111 What’s Linear Algebra? What is linear algebra? Naively, linear algebra = linear + algebra Linear Algebra Math1111 What’s Linear Algebra? What is linear algebra? Naively, linear algebra = linear + algebra Linear  concern with straight lines or its properties. Algebra  "a branch of mathematics concerning the study of structure, relation and quantity" [Wikipedia] Linear Algebra Math1111 What’s Linear Algebra?...
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 Spring '10
 Dr,Li
 Math, Linear Algebra, Algebra

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