# Lectures on Linear Algebra by I.M. Gel'Fand; Translator A. Shenitzer

By I.M. Gel'Fand; Translator A. Shenitzer

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Additional resources for Lectures on Linear Algebra

Example text

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 , .