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x'  or  t(x), where x is a matrix

Keywords: matrix algebra, operations
x' (x followed by a single quote or "prime") computes the transpose of x
if x is a matrix, that is the matrix y with y[i,j] = x[j,i].

When x is a vector of length n, x' is a 1 by n matrix, that is, a row

When x is an array with dimensions n1, n2, ..., nk, y <- x' computes an
array y with dimensions nk, ..., n1 such that y[i1,...,ik] is
x[ik,...,i1].  When x is a generalized matrix (see 'matrices'), so is
x', and matrix(x)' = matrix(x').

t(x) is synonymous with x'.

Provided ndims(x) > 1, t(x,run(ndims(x),1)) is equivalent to t(x) and
x'.  See also t().

Instead of x' %*% y and x %*% y' you can use x %c% y and x %C% y,
respectively which use less internal memory.  See topic 'matrices' for
more information on these matrix multiplication operators.

When x is a structure, each of whose components is REAL, LOGICAL, or
CHARACTER, x' computes a structure with the same shape and with the same
component names as x whose non-structure components are the transposes
of the corresponding components of x.

See also topics array(), 'matrices', 'subscripts'.

Gary Oehlert 2003-01-15