solve {base}R Documentation

Solve a System of Equations


This generic function solves the equation a %*% x = b for x, where b can be either a vector or a matrix.


solve(a, b, ...)

## Default S3 method:
solve(a, b, tol, LINPACK = FALSE, ...)


a a square numeric or complex matrix containing the coefficients of the linear system.
b a numeric or complex vector or matrix giving the right-hand side(s) of the linear system. If missing, b is taken to be an identity matrix and solve will return the inverse of a.
tol the tolerance for detecting linear dependencies in the columns of a. If LINPACK is TRUE the default is 1e-7, otherwise it is .Machine$double.eps. Future versions of R may use a tighter tolerance. Not presently used with complex matrices a.
LINPACK logical. Should LINPACK be used (for compatibility with R < 1.7.0)? Otherwise LAPACK is used.
... further arguments passed to or from other methods


a or b can be complex, but this uses double complex arithmetic which might not be available on all platforms and LAPACK will always be used.

The row and column names of the result are taken from the column names of a and of b respectively. As from R 1.7.0 if b is missing the column names of the result are the row names of a. No check is made that the column names of a and the row names of b are equal.

For back-compatibility a can be a (real) QR decomposition, although qr.solve should be called in that case. qr.solve can handle non-square systems.


Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

solve.qr for the qr method, chol2inv for inverting from the Choleski factor backsolve, qr.solve.


hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
h8 <- hilbert(8); h8
sh8 <- solve(h8)
round(sh8 %*% h8, 3)

A <- hilbert(4)
A[] <- as.complex(A)
## might not be supported on all platforms

[Package base version 2.5.0 Index]