Consider annxn matrix A with m distinct eigenvalues Ai,..., Xm. Show that matrix A is
Chapter 7, Problem 70(choose chapter or problem)
Consider annxn matrix A with m distinct eigenvalues Ai,..., Xm. Show that matrix A is diagonalizable if (and only if) (A - k i I n) ( A - k 2l)---(A -kml) = 0. (Hint: If (A - X, In)(A - k2l) (A kmIn) = 0. use Exercise 4.2.83 to show that the sum of the dimensions of the eigenspaces is n.)
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