Archive for March, 2008

Matrices and Magic Squares

In MATLAB, a matrix is a rectangular array of numbers. Special meaning is sometimes attached to 1-by-1 matrices, which are scalars, and to matrices with only one row or column, which are vectors. MATLAB has other ways of storing both numeric and nonnumeric data, but in the beginning, it is usually best to think of everything as a matrix. The operations in MATLAB are designed to be as natural as possible. Where other programming languages work with numbers one at a time, MATLAB allows you to work with entire matrices quickly and easily. A good example matrix, used throughout this book, appears in the Renaissance engraving Melancholia I by the German artist and amateur mathematician Albrecht Dürer. (more…)

This section provides an introduction to MATLAB’s desktop tools. You can also use MATLAB functions to perform most of the features found in the desktop tools. The tools are:

•“Command Window”
•“Command History”
•“Launch Pad”
•“Help Browser”
•“Current Directory Browser”
•“Workspace Browser”
•“Array Editor”
•“Editor/Debugger”

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while Repeat statements an indefinite number of times.
The general form of a while statement is:

while expression
statements
END

The statements are executed while the real part of the expression
has all non-zero elements. The expression is usually the result of
expr rop expr where rop is ==, <, >, <=, >=, or ~=.

The BREAK statement can be used to terminate the loop prematurely.

For example (assuming A already defined):

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E = 0*A; F = E + eye(size(E)); N = 1;
while norm(E+F-E,1) > 0,
E = E + F;
F = A*F/N;
N = N + 1;
end

See also for, if, switch, break, end.