Matlab

Matrices

Basics

See Introduction to Matlab

Special matrices/vectors

Name (matrix type)	Matlab syntax	Result
Ones	>> ones(3,2);	$ \left[ \begin{array}{cc} 1 & 1 \\ 1 & 1 \\ 1 & 1 \end{array} \right] $
Zeros	>> zeros(3,1);	$ \left[ \begin{array}{cc} 0 \\ 0 \\ 0 \end{array} \right] $
Eye (identity)	>> eye(3);	$ \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] $
Rand (random numbers)	>> rand(3,2);	$ \left[ \begin{array}{cc} 0.21955 & 0.27560\\ 0.42385 & 0.62212\\ 0.53343 & 0.69182 \end{array} \right] $
Meshgrid	>> [x,y] = meshgrid(1:4,1:4);	$ x = \left[ \begin{array}{cccc} 1& 2& 3& 4\\ 1& 2& 3& 4\\ 1& 2& 3& 4\\ 1& 2& 3& 4 \end{array} \right] $ $ y = \left[ \begin{array}{cccc} 1& 1& 1& 1\\ 2& 2& 2& 2\\ 3& 3& 3& 3\\ 4& 4& 4& 4 \end{array} \right] $
Magic (magic square matrix) (The sum of each row and column is equal to the same value)	>> magic(4);	$ \left[ \begin{array}{cccc} 16& 2& 3& 13\\ 5& 11& 10& 8\\ 9& 7& 6& 12\\ 4& 14& 15& 1 \end{array} \right] $
Linspace	>> linspace(A,B,N)	$ \left[ A + \frac{i}{n-1} B \right] \qquad i=0, \dots, N-1 $
Logspace	>> logspace(A,B,N)	$ \left[ 10^{A} + 10^{ \frac{i}{n-1} B } \right] \qquad i=0, \dots, N-1 |} == Functions == linspace logspace {|class="wikitable" !Function name !Matlab syntax/output |- |det |Returns the determinant of a matrix: <syntaxhighlight lang="matlab"> >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> det(A) ans = -1.4495e-12 </syntaxhighlight> |- |find | |- |flipud | |- |fliplr | |- |length | |- |max | |- |min | |- |repmat |This function creates a new matrix consisting of several copies of an existing matrix. <syntaxhighlight lang="matlab"> >> A = magic(3) A = 8 1 6 3 5 7 4 9 2 >> repmat(A,2,2) ans = 8 1 6 8 1 6 3 5 7 3 5 7 4 9 2 4 9 2 8 1 6 8 1 6 3 5 7 3 5 7 4 9 2 4 9 2 </syntaxhighlight> |- |size | |- |sort | |} == Operators == ===Addition, subtraction=== Addition/subtraction can be done with vectors or matrices as with numbers: <syntaxhighlight lang="matlab"> >> A=ones(2,3) A = 1 1 1 1 1 1 >> B=ones(2,3) B = 1 1 1 1 1 1 >> C = A + B C = 2 2 2 2 2 2 >> C = A - B C = 0 0 0 0 0 0 </syntaxhighlight> ===Multiplication, division=== Multiplication of matrices requires that the inner dimensions must match (i.e. <math>M \times N) * (N \times P) $): >> A A = 0.85645 0.86793 0.39228 0.22329 0.82611 0.40042 0.79097 0.45921 0.30861 >> B B = 0.976938 0.200895 0.239939 0.300156 0.205414 0.963250 0.396226 0.425022 0.041877 >> C = A*B C = 1.25264 0.51707 1.05796 0.62476 0.38474 0.86609 1.03284 0.38440 0.64504 Division of matrices is defined as $ A/B = A B^{-1} $: >> A = rand(3,3) A = 0.85645 0.86793 0.39228 0.22329 0.82611 0.40042 0.79097 0.45921 0.30861 >> B = rand(3,3) B = 0.976938 0.200895 0.239939 0.300156 0.205414 0.963250 0.396226 0.425022 0.041877 >> >> C = A/B C = 0.015664 0.321640 1.879233 -0.763591 0.516569 2.054946 0.435077 0.177713 0.788906 >> C = A*inv(B) C = 0.015664 0.321640 1.879233 -0.763591 0.516569 2.054946 0.435077 0.177713 0.788906 Component-wise multiplication and division can also be done: >> A A = 0.85645 0.86793 0.39228 0.22329 0.82611 0.40042 0.79097 0.45921 0.30861 >> B B = 0.976938 0.200895 0.239939 0.300156 0.205414 0.963250 0.396226 0.425022 0.041877 >> C = A.*B C = 0.836694 0.174363 0.094122 0.067023 0.169693 0.385709 0.313402 0.195175 0.012924 >> C = A./B C = 0.87666 4.32032 1.63489 0.74392 4.02167 0.41570 1.99626 1.08044 7.36944 Input/output Switches Functions Graphics Examples Fluid mechanics Heat transfer Optimization Statistics See also Octave Introduction to Matlab (lecture)