lecture_36 - MA 36600 LECTURE NOTES: WEDNESDAY, APRIL 22...

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Unformatted text preview: MA 36600 LECTURE NOTES: WEDNESDAY, APRIL 22 Fundamental Matrices Diagonalizable Matrices. We explain how to exponentiate an arbitrary matrix. First, we consider a special case. We say that an n n matrix is a diagonal matrix if it is in the form D = r 1 r 2 . . . . . . . . . . . . r n . We will show that the exponential of a diagonal matrix is the diagonal matrix exp( D t ) = e r 1 t e r 2 t . . . . . . . . . . . . e r n t . First, note that the product of two n n diagonal matrices is again an n n diagonal matrix: D (1) = r (1) 1 r (1) 2 . . . . . . . . . . . . r (1) n and D (2) = r (2) 1 r (2) 2 . . . . . . . . . . . . r (2) n give the product D (1) D (2) = r (1) 1 r (2) 1 r (1) 2 r (2) 2...
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This note was uploaded on 05/24/2011 for the course MA 36600 taught by Professor Ma during the Spring '09 term at Purdue University-West Lafayette.

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lecture_36 - MA 36600 LECTURE NOTES: WEDNESDAY, APRIL 22...

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