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Matrix equivalence

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Definition of equivalent matrices
A matrix of rank k is equivalent to a matrix with 1 in the first k diagonal entries and 0 elsewhere.
Two matrices of the same size are equivalent if and only if they have the same rank.
Equivalent matrices represent the same linear transformation with resect to appropriate bases.

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A matrix of rank k is equivalent to a matrix with 1 in the first k diagonal entries and 0 elsewhere.

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