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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]