Consistent iff rank(A, b) = rank(A); with full column rank the solution is
unique (A^-1 b when square) or, when inconsistent, the least-squares
(A'A)^-1 A'b, both by QR (Hedderich, Sachs & Reynarowych 2023, eqs
2.47-2.50). A rank-deficient A gives x = NULL.
Usage
linsys(A, b, tol = 1e-07)
Arguments
- A
n x m matrix.
- b
Right-hand side.
- tol
Rank tolerance.
Value
Named list: x, rank_A, rank_Ab, consistent, kind, rss.
References
Golub, G. H. & Van Loan, C. F. (2013). Matrix Computations,
sec. 5.3.
Examples
linsys(matrix(c(2, 1, -1, -3, -1, 2, -2, 1, 2), 3, byrow = TRUE), c(8, -11, -3))$x
#> [1] 2 3 -1
