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    %% Matrices and Arrays
% _MATLAB_ is an abbreviation for "matrix laboratory." While other
% programming languages mostly work with numbers one at a time, MATLAB(R) is
% designed to operate primarily on whole matrices and arrays.
%
% All MATLAB variables are multidimensional _arrays_, no matter what type of
% data. A _matrix_ is a two-dimensional array often used for linear algebra.

% Copyright 2015 The MathWorks, Inc.


%% Array Creation
% To create an array with four elements in a single row, separate the
% elements with either a comma (|,|) or a space.
a = [1 2 3 4]
%%
% This type of array is a _row vector_.
%%
% To create a matrix that has multiple rows, separate the rows with
% semicolons.
a = [1 2 3; 4 5 6; 7 8 10]

%%
% Another way to create a matrix is to use a function, such as |ones|,
% |zeros|, or |rand|. For example, create a 5-by-1 column vector of
% zeros.
z = zeros(5,1)

%% Matrix and Array Operations
% MATLAB allows you to process all of the values in a matrix using a single
% arithmetic operator or function.
a + 10
%%
sin(a)

%%
% To transpose a matrix, use a single quote (|'|):
a'

%%
% You can perform standard matrix multiplication, which computes the inner
% products between rows and columns, using the |*| operator. For example,
% confirm that a matrix times its inverse returns the identity matrix:
p = a*inv(a)

%%
% Notice that |p| is not a matrix of integer values. MATLAB stores numbers as
% floating-point values, and arithmetic operations are sensitive to small
% differences between the actual value and its floating-point
% representation. You can display more decimal digits using the |format|
% command:
format long
p = a*inv(a)

%%
% Reset the display to the shorter format using
format short
%%
% |format| affects only the display of numbers, not the way MATLAB computes
% or saves them.

%%
% To perform element-wise multiplication rather than matrix multiplication,
% use the |.*| operator:
p = a.*a

%%
% The matrix operators for multiplication, division, and power each have a
% corresponding array operator that operates element-wise. For example,
% raise each element of |a| to the third power:
a.^3

%% Concatenation
% _Concatenation_ is the process of joining arrays to make larger ones. In
% fact, you made your first array by concatenating its individual elements.
% The pair of square brackets |[]| is the concatenation operator.
A = [a,a]

%%
% Concatenating arrays next to one another using commas is called
% _horizontal_ concatenation. Each array must have the same number of rows.
% Similarly, when the arrays have the same number of columns, you can
% concatenate _vertically_ using semicolons.
A = [a; a]

%% Complex Numbers
% Complex numbers have both real and imaginary parts, where the imaginary
% unit is the square root of |-1|.
sqrt(-1)

%%
% To represent the imaginary part of complex numbers, use either |i| or |j| .
c = [3+4i, 4+3j; -i, 10j]