Kunze Linear Algebra · Problem 6.2.6

Elementary Canonical Forms

Mathematics — Methods · diagonalizability-conditions

Problem

Let TT be the linear operator on R4R^4 which is represented in the standard ordered basis by the matrix [0000a0000b0000c0].\begin{bmatrix} 0 & 0 & 0 & 0 \\ a & 0 & 0 & 0 \\ 0 & b & 0 & 0 \\ 0 & 0 & c & 0 \end{bmatrix}. Under what conditions on aa, bb, and cc is TT diagonalizable?

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