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Matrices and Mag ic Squares

and

sum(diag(A))

produces

ans =

The other diagonal, the so-called antidiagonal, is not so important

mathematically, so MATLAB does not have a ready-made function for it.

But a function originally intended for use in graphics,

fliplr,flipsamatrix

from left to right:

sum(diag(fliplr(A)))

ans =

You h ave verified that the matrix in Dürer’s en graving is indeed a magic

square and, in the process, have sampled a few MATLAB matrix operations.

The following sections continue to use this m atrix to illustrate additional

MATLAB capabilities.

Subscripts

The element in row i and column j of A is d e n o ted by A(i,j). For example,

A(4,2) is the number in the fourth row and second column. For our m agic

square,

A(4,2) is 15. So to compute the sum of the elements in the fourth

column of

A,type

A(1,4) + A(2,4) + A(3 ,4) + A(4,4)

This produces

ans =

but is not the most elegant way of summing a single column.

It is also possible to refer to the elements of a matrix with a single subscript,

A(k). This is the usual way of referencing row and column vectors. But it

can a lso apply to a fully two-dimensional m atrix, in which case the array is

2-7

1 2 ... 24 25 26 27 28 29 30 31 32 33 34 ... 239 240

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MATLAB POLYSPACE RELEASE NOTES Manuale Utente Pagina 29