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F denotes a field

V denotes a vector space over F

L(V) denotes a vector space whose members are linear operators from V to V itself and its field is F, then L(V) is an algebra where multiplication is composition of functions.

τ denotes a linear operator contained in L(V)

ι denotes the multiplicative identity of L(V)

Question:

Why is n^{2}+ 1 vectors:

ι, τ, τ^{2}, ... ,τ^{n2}

are linearly dependent in L(V)?

I wonder why, if these vectors are linear dependent, then one of them can be expressed as the linear combination of other vectors, but how?

Thanks for any help!

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# About the linear dependence of linear operators

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