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 square numeric or complex matrix containing the coefficients of the linear system. Logical matrices are coerced to numeric.


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.


the tolerance for detecting linear dependencies in the columns of a. The default is .Machine$double.eps. Not currently used with complex matrices a.


logical. Defunct and ignored.


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.

The row and column names of the result are taken from the column names of a and of b respectively. 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.

Unsuccessful results from the underlying LAPACK code will result in an error giving a positive error code: these can only be interpreted by detailed study of the FORTRAN code.


The default method is an interface to the LAPACK routines DGESV and ZGESV.

LAPACK is from


Anderson. E. and ten others (1999) LAPACK Users' Guide. Third Edition. SIAM.
Available on-line at

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 3.3.2 Index]