MATLAB POLYSPACE RELEASE NOTES Bedienungsanleitung PDF herunterladen (Seite 27)

Matrices and Mag ic Squares

MATLAB displays the matrix you just ente red:

163213

51011 8

96712

41514 1

This matrix matches the num bers in the engraving. Once you have entered

the matrix, it is automatically remembered in the M ATLAB w orkspace. You

can r efer to it simply as

A.NowthatyouhaveA intheworkspace,takealook

at what makes it so interesting. W hy is it magic?

sum, transpose, and diag

You are probably already aware that the special properties o f a magic square

have to do with the various ways of summing its elements. If y ou take the

sum along any row or column, or along either of the two main diagonals,

you will always get the same number. Let us verify that using M ATLAB.

The first statem ent to try is

sum(A)

MATLAB replies with

ans =

34 34 34 34

When you do not specify an output variable, MATLAB uses the variable ans,

short for answer, to store the results of a calculation. You have computed a

row vector containing the sums of the columns of

A. Sure enough, each of the

columnshasthesamesum,themagic sum, 34.

How about the row sums? MATLAB has a p reference for working with the

columnsofamatrix,soonewaytogettherowsumsistotransposethe

matrix, compute the column sums of the transpose, and then transpose the

result. For an additional way that avoids the double transpose use the

dimension argument for the

sum function.

MATLAB has two transpose operators. The apostrophe operator (e.g.,

A')

performs a complex conjugate transposition. It flips a matrix about its main

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MATLAB POLYSPACE RELEASE NOTES Bedienungsanleitung Seite 27