Info Catalog calc: Infinities calc: Data Types calc: Strings

calc: Vectors and Matrices

 
 5.6 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.  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; 
 Basic Arithmetic and 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’.
 

Info Catalog calc: Infinities calc: Data Types calc: Strings