Matrices in R
This section provides details on the construction and manipulation of these objects, including matrix facilities that are different from typical element-wise operations.
Matrices
Linear equations and inversion
Solving linear equations is the inverse of matrix multiplication. When after
> b <- A %*% x
only A and b are given, the vector x is the
solution of that linear equation system. In R,
> solve(A,b)
solves the system, returning x (up to some accuracy loss).
Note that in linear algebra, formally
x = A^{-1} %*% b
where
A^{-1} denotes the inverse of
A, which can be computed by
solve(A)
but rarely is needed. Numerically, it is both inefficient and
potentially unstable to compute x <- solve(A) %*% b instead of
solve(A,b).
The quadratic form x %*% A^{-1} %*% x which is used in multivariate computations, should be computed by
something like17 x %*% solve(A,x), rather
than computing the inverse of A.