Vol. 49, No. 2, 1973

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On the maximal number of linearly independent real vectors annihilated simultaneously by two real quadratic forms

Frank Uhlig

Vol. 49 (1973), No. 2, 543–560

For a nonsingular pair of real symmetric (r.s.) matrices S and T the maximal number m of lin. ind. vectors simultaneously annihilated by the associated quadratic forms is computed as a function of the real Jordan normal form of S1T. Conversely one can deduce which real Jordan normal form S1T must have, if a specific m is the maximal number of such vectors. Furthermore, two new conditions are found that assure S and T to be simultaneously diagonalizable by a real congruence transformation.

Mathematical Subject Classification 2000
Primary: 15A21
Received: 12 July 1972
Published: 1 December 1973
Frank Uhlig