Vectors and Matrices
====================

The "vector" data type is flexible and general.  A vector is simply a
list of zero or more data objects.  When these objects are numbers,
the whole is a vector in the mathematical sense.  When these objects
are themselves vectors of equal (nonzero) length, the whole is a
"matrix".  A vector which is not a matrix is referred to here as a
"plain vector".

A vector is displayed as a list of values separated by commas and enclosed
in square brackets:  `[1, 2, 3]'.  Thus the following is a 2 row by
3 column matrix:  `[[1, 2, 3], [4, 5, 6]]'.  Vectors, like complex
numbers, are entered as incomplete objects.  See Incomplete Objects.
During algebraic entry, vectors are entered all at once in the usual
brackets-and-commas form.  Matrices may be entered algebraically as nested
vectors, or using the shortcut notation `[1, 2, 3; 4, 5, 6]',
with rows separated by semicolons.  The commas may usually be omitted
when entering vectors:  `[1 2 3]'.  Curly braces may be used in
place of brackets: `{1, 2, 3}', but the commas are required in
this case.

Traditional vector and matrix arithmetic is also supported;
See Basic Arithmetic and See Matrix Functions.
Many other operations are applied to vectors element-wise.  For
example, the complex conjugate of a vector is a vector of the complex
conjugates of its elements.

Algebraic functions for building vectors include `vec(a, b, c)' to
build `[a, b, c]', `cvec(a, n, m)' to build an NxM matrix of `a's, and
`index(n)' to build a vector of integers from 1 to `n'.