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24 Feb 2022
Show that A v = lambda v rightarrow (cos t A) v, (sin t A) v = (sin t lambda) v. Compute cos t A and sin t A in each of the following cases: A = (0 1 1 0), A = (0 1 -1 0), A = (1 0 1 1), A = (0 i i 0). Suppose A belongsto M(n, C) and B = (0 A -A 0) belongsto M(2n, C). Show that e^tB = (cost A sin t A -sin t A cos t A).
Show that A v = lambda v rightarrow (cos t A) v, (sin t A) v = (sin t lambda) v. Compute cos t A and sin t A in each of the following cases: A = (0 1 1 0), A = (0 1 -1 0), A = (1 0 1 1), A = (0 i i 0). Suppose A belongsto M(n, C) and B = (0 A -A 0) belongsto M(2n, C). Show that e^tB = (cost A sin t A -sin t A cos t A).
25 Feb 2022
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