Lect1 - Linear Algebra Math1111 What’s the use of Linear...

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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 input-output 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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Lect1 - Linear Algebra Math1111 What’s the use of Linear...

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