Page 249 - Determinants and Their Applications in Mathematical Physics
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234 5. Further Determinant Theory
It follows that there exist at least two solutions of the equation
|X + Y| = |X| + |Y|, n =2,
namely
2
2
X = PQ + QP or P − Q ,
Y = PQ − QP.
Furthermore, the equation
|X − Y + Z| = |X|−|Y| + |Z|, n =2,
is satisfied by
2
2
X = P − Q ,
Y = PQ + QP,
Z =2PQ.
Are there any other determinantal identities of a similar nature?
