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Wednesday, May 5, 2010

M208 TMA03 Question 4

Done in draft. Question about finding an orthogonal base of some abstract vector space. Not really difficult considering the marks assigned ( 20 ).

In MST121 / MS221 we learned to find the closed form for the Fibonacci sequence. Or solving the recurrence equation $a_{n} - a_{n-1} - a_{n-2} = 0$, equations of this type are called homogenous linear recurrence equations ( of the second order ). Inhomogenous equations have a function of n on the RHS. An inhomogenous recurrence equation of the first order is for example $a_{n} = 2 a_{n-1} + n$. The solutions of this equation consist of a homonegenous part and a particular part. ( More later. )

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Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)