# scalar matrix

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Related to scalar matrix: symmetric matrix
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 Noun 1 scalar matrix - a diagonal matrix in which all of the diagonal elements are equaldiagonal matrix - a square matrix with all elements not on the main diagonal equal to zeroidentity matrix, unit matrix - a scalar matrix in which all of the diagonal elements are unity
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Then for all scalar matrix a = [([a.sub.i]).sub.i[member of]M(m,n)],
Assume that a + [alpha]c is not a scalar matrix. By Lemma 5, we can assume that a + [alpha]c and q have all nonzero entries, say a + [alpha]c = [[summation].sub.kl][t.sub.kl][e.sub.kl] and q = [[summation].sub.kl][q.sub.kl][e.sub.kl], for 0 [not equal to] [t.sub.kl], 0 [not equal to] [q.sub.kl] [member of] K.
Spectral matrix in (11) becomes a scalar matrix. Rank of [(u v).sup.T] is now reduced and u + sv = 0 for scalar s [not equal to] 0.

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