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Defining t7 AB = cr [A 6 BI, 6 AB : 6 TM O "BI (1.5) these quantities satisfy [era,, ac,] = 2(g,C ~aD _ gaC ~rnO + gad ~BC _ gad crnC)t [6aB, 6CD] = 2(gnC sAD _ gaC 6rid + gaD 6BC gad ...
Hence rr(AB) £ rr(B) and cr(AB) £ cr(A), from which the result follows. # Theorem. r(A+B) £ r(A) + r(B). Proof. Row space of A + B is contained in the span of the rows of A and B ...
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Defining t7 AB = cr [A 6 BI, 6 AB : 6 TM O "BI (1.5) these quantities satisfy [era,, ac,] = 2(g,C ~aD _ gaC ~rnO + gad ~BC _ gad crnC)t [6aB, 6CD] = 2(gnC sAD _ gaC 6rid + gaD ...
Hence rr(AB) £ rr(B) and cr(AB) £ cr(A), from which the result follows. # Theorem. r(A+B) £ r(A) + r(B). Proof. Row space of A + B is contained in the span of the rows of A ...
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