[lin.alg] [tricks]

has characteristic polynomial .

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[lin.alg] [tricks]

has characteristic polynomial .

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[lin.alg]

Let be a -vector space, then as vector spaces. (Abusing notation and treating as a 1D vector space over in the definition of ).

is a vector space. Easy to check that where is the single basis vector in is a linear transformation. It is surjective: is a linear map. It is injective: if then , i.e. .