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Problem related to ring homomorphism

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Reference no: EM131588436

Question: It is possible to associate with each periodic sequence of period N an N x N circulant matrix. This matrix is defined by taking the given values of the sequence as the first row of the matrix, and filling in the remaining rows by means of a cyclic shift of the first row. The matrix associated with 1 is

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Prove that Mf.Mg = M[f*g] and c1Mf + c2Mg = M[c1f + c2g], showing that the mapping from periodic sequences to circulant matrices is a ring homomorphism.

Reference no: EM131588436

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