Question
Let V = Mn(R), A be a fixed nn matrix, and T: V V be the linear map defined by T(B) = AB. i.
Let V = Mn(R), A be a fixed n×n matrix, and T: V −→ V be the linear map defined by T(B) = AB.
i. Show that the minimal polynomial for T is the minimal polynomial for A.
ii. Show that if A is diagonalizable over R, then T is diagonalizable.
Step by Step Solution
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Step: 1
i The minimal polynomial of A mAt is a monic polynomial of degree n such that mA...
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Applied Linear Algebra
Authors: Peter J. Olver, Cheri Shakiban
1st edition
131473824, 978-0131473829
