Powers
If n is a natural number, the nth power of a matrix in Jordan normal form will be a direct sum of upper triangular matrices, as a result of block multiplication. More specifically, after exponentiation each Jordan block will be an upper triangular block.
For example,
Further, each triangular block will consist of λn on the main diagonal, times λn-1 on the upper diagonal, and so on. This expression is valid for negative integer powers as well if one extends the notion of the binomial coefficients .
For example,
Read more about this topic: Jordan Normal Form
Famous quotes containing the word powers:
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—James Madison (17511836)
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—Thomas Jefferson (17431826)
“To receive applause for works which do not demand all our powers hinders our advance towards a perfecting of our spirit. It usually means that thereafter we stand still.”
—G.C. (Georg Christoph)