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<A NAME=MATRIX>

<TITLE>MATRIX</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>MATRIX</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>declaration</B><P>
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Identifiers are declared to be of type <em>matrix</em>. 
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syntax: </H3>
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<em>matrix</em>&lt;identifier&gt;  _ _ _ option (&lt;index&gt;,&lt;index&gt;) 
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{,&lt;identifier&gt;  _ _ _ option 
 (&lt;index&gt;,&lt;index&gt;)}* 
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&lt;identifier&gt; must not be an already-defined operator or array or 
the name of a scalar variable. Dimensions are optional, and if used appear 
inside parentheses. &lt;index&gt; must be a positive integer. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
matrix a,b(1,4),c(4,4); 

b(1,1); 

  0 


a(1,1); 

  ***** Matrix A not set 


a := mat((x0,y0),(x1,y1)); 

  A(1,1) := X0
  A(1,2) := Y0
  A(2,1) := X0
  A(2,2) := X1


length a; 

  {2,2} 


b := a**2; 

              2
  B(1,1) := X0  + X1*Y0
  B(1,2) := Y0*(X0 + Y1)
  B(2,1) := X1*(X0 + Y1)
                      2
  B(2,2) := X1*Y0 + Y1

</TT></PRE><P>When a matrix variable has not been dimensioned, matrix elements c
annot be 
referenced until the matrix is set by the 
<A HREF=r37_0343.html>mat</A> operator. When a 
matrix is dimensioned in its declaration, matrix elements are set to 0. 
Matrix elements cannot stand for themselves. When you use 
<A HREF=r37_0199.html>let</A> on 
a matrix element, there is no effect unless the element contains a 
constant, in which case an error message is returned. The same behavior 
occurs with 
<A HREF=r37_0189.html>clear</A>. Do &lt;not&gt; use 
<A HREF=r37_0189.html>clear</A> to try to 
set a matrix element to 0. 
<A HREF=r37_0199.html>let</A> statements can be applied to 
matrices as a whole, if the right-hand side of the expression is a matrix 
expression, and the left-hand side identifier has been declared to be a matrix. 

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Arithmetical operators apply to matrices of the correct dimensions. The 
operators <em>+</em> and <em>-</em> can be used with matrices of the same 
dimensions. The operator <em>*</em> can be used to multiply 
m x n matrices by n x p 
matrices. Matrix multiplication is non-commutative. Scalars can also be 
multiplied with matrices, with the result that each element of the matrix 
is multiplied by the scalar. The operator <em>/</em> applied to two 
matrices computes the first matrix multiplied by the inverse of the 
second, if the inverse exists, and produces an error message otherwise. 
Matrices can be divided by scalars, which results in dividing each element 
of the matrix. Scalars can also be divided by matrices when the matrices 
are invertible, and the result is the multiplication of the scalar by the 
inverse of the matrix. Matrix inverses can by found by <em>1/A</em> or 
<em>/A</em>, where <em>A</em> is a matrix. Square matrices can be raised to 
positive integer powers, and also to negative integer powers if they are 
nonsingular. 
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When a matrix variable is assigned to the results of a calculation, the 
matrix is redimensioned if necessary. 
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