(octave.info)Creating Diagonal Matrices

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21.1.1 Creating Diagonal Matrices
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The most common and easiest way to create a diagonal matrix is using the
built-in function “diag”.  The expression ‘diag (v)’, with V a vector,
will create a square diagonal matrix with elements on the main diagonal
given by the elements of V, and size equal to the length of V.  ‘diag
(v, m, n)’ can be used to construct a rectangular diagonal matrix.  The
result of these expressions will be a special diagonal matrix object,
rather than a general matrix object.

   Diagonal matrix with unit elements can be created using “eye”.  Some
other built-in functions can also return diagonal matrices.  Examples
include “balance” or “inv”.

   Example:

       diag (1:4)
     ⇒
     Diagonal Matrix

        1   0   0   0
        0   2   0   0
        0   0   3   0
        0   0   0   4

       diag (1:3,5,3)

     ⇒
     Diagonal Matrix

        1   0   0
        0   2   0
        0   0   3
        0   0   0
        0   0   0