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Unformatted text preview: ( unique linear combination) What is the condition in R 3 ? in R n ? algebraically, this means that u and v are nonzero vectors, and u ≠ c v . 3 ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = n n v v v A # " 2 1 2 1 ] [ a a a v If we write , then it is like a “dot product”. Example: then Property: A = and O v = for any A and v . Example: Property: Sometimes I n is simply written as I (any size). i th entry 4 Example: stochastic matrix probability matrix of a sample person’s residence movement nonnegative entries, unity column sums : current population of the city and suburbs : population distribution in the next year : population distribution in the year following the next Example: rotation matrix Proof for (e): If B ≠ A , then ( B − A ) e j ≠ , i.e., B e j ≠ A e j , for some j . 3...
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This note was uploaded on 10/16/2010 for the course EE [email protected] taught by Professor Fong during the Spring '09 term at National Taiwan University.
 Spring '09
 Fong

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