# Invariant Theory by John Fogarty

By John Fogarty

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If SP is replaced by DP then the precision is set to double precision. mod module of LAPACK95. All driver routine interfaces are contained in this module. Statement 7 defines arguments A and B to be allocatable real single-precision arrays. The program works in complex arithmetic if REAL(WP) is replaced by COMPLEX(WP). Statements 9-11 allocate A and B and assign data to these arrays. Statement 12 calls LA_GESV to solve the system. On exit, the solution matrix X is stored in array B. 1: Example program calling an LAPACK95 driver routine.

Mod module of LAPACK95. All driver routine interfaces are contained in this module. Statement 7 defines arguments A and B to be allocatable real single-precision arrays. The program works in complex arithmetic if REAL(WP) is replaced by COMPLEX(WP). Statements 9-11 allocate A and B and assign data to these arrays. Statement 12 calls LA_GESV to solve the system. On exit, the solution matrix X is stored in array B. 1: Example program calling an LAPACK95 driver routine. Example 2 The program in Fig.

22 Chapter 2. Contents of LAPACK95 EI and £2 have the following detailed structures, depending on whether m — r > 0 or m — r < 0. In the first case, m — r > 0, then Here / is the rank of 5, k — r — /, C and 5 are diagonal matrices satisfying C2 + S2 = /, and S is nonsingular. , /. , otk//3k are infinite, and the remaining / generalized singular values are finite. In the second case, when m — r < 0, and Again, / is the rank of B, k — r — /, C and S are diagonal matrices satisfying C2 + S2 = /, 5 is nonsingular, and we may identify a\ = • • • = otk = 1, &k+i — ca for i = l , .