1 %% Vector basics
   2 
   3 % Row vector
   4 x = [1 1 1 1]
   5 
   6 % Column vector
   7 y = [1 1 1 1]'
   8 
   9 % create vector with sequence of numbers
  10 z = [1:2:10]
  11 z = [-1:0.01:1]
  12 
  13 % Getting an element out of a vector
  14 z(2)
  15 z(2:3)
  16 
  17 % looping over elements
  18 for i = 1:4,
  19     display( x(i) );
  20 end;
  21 
  22 % Add or multiply values etc.
  23 x + 10
  24 2*x
  25 
  26 
  27 %% Vector multiplication
  28 % Transpose vectors
  29 x
  30 x'
  31 
  32 % Vector multiplication: row vector * column vector (for time being)
  33 x,y    % just for display
  34 x*y
  35 
  36 % Common error: multiply vectors of different lengths:
  37 z = [1 1 1]'
  38 x*z
  39 
  40 % Define two parallel vectors:
  41 x = [1 0 1 0]
  42 y = [1 0 1 0]'
  43 
  44 % Multiply vectors
  45 x*y
  46 
  47 % Define two orthogonal vectors:
  48 x = [1 0 1 0]
  49 y = [0 1 0 1]'
  50 
  51 % Multiply vectors
  52 x*y
  53 
  54 
  55 %% Some things you can do with vectors 
  56 % Define a vector
  57 x = [1 2 3 4]
  58 
  59 % Define another vector
  60 y = [0 0 1 0]'   % note the transpose
  61 
  62 % Multiply the vectors
  63 x*y
  64 
  65 % Define another vector
  66 z = [1 1 1 1]'
  67 
  68 % Sum of elements of x:
  69 x*z
  70 
  71 % Average of elements of x
  72 % length(x) yields the number of elements of a vector
  73 x*z / length(x)
  74 
  75 % Define another vector
  76 y = [1 -1 1 -1]'
  77 
  78 % Subtract sum of even from sum of odd elements in x:
  79 x*y
  80 
  81 clear
  82 %% Matrices
  83 
  84 % Define a (diagonal) matrix
  85 x = [1 1 1; 2 2 2]
  86 
  87 % Getting elements out of matrices
  88 x(1,2)
  89 x(:,1)
  90 x(2,:)
  91 
  92 % Getting matrix dimensions
  93 size(x) % returns number of rows and columns, respectively
  94 [m,n] = size(x)
  95 
  96 %% Matrices c'd
  97 % Matrix transpose
  98 x
  99 y = x'
 100 
 101 % adding/multiplying values etc.
 102 x + 2
 103 2 * x
 104 
 105 % Define another matrix
 106 z = [1 2 3; 4 5 6]
 107 
 108 % Subtract z from x
 109 x - z
 110 
 111 % Add z to x
 112 x + z
 113 
 114 % Elementwise multiplication (NOT "matrix multiplication": "*")
 115 x .* z
 116 
 117 % Try... (matrix multiplication)
 118 x * z
 119 
 120 % Elementwise division (NOT "matrix division/inversion": "/")
 121 x ./ z
 122 
 123 % Try... (matrix inversion)
 124 x / z
 125 
 126 %% Multiplying matrix and vector
 127 % Define a vector
 128 v = [1 1 1]'
 129 
 130 % Mutliply matrix x with vector v (and obtain sum within each row of x)
 131 x
 132 v
 133 x * v
 134 
 135 % matrix and vector dimensions must agree
 136 v * x % does not work
 137 
 138 %% interpretation as sum of column vectors
 139 % x * v results in the sum of column vectors in x
 140 x * v
 141 1*x(:,1) + 1*x(:,2) + 1*x(:,3)
 142 
 143 %% Matrix multiplication
 144 % Multiply two matrices
 145 x * y
 146 
 147 % Multiply two matrices
 148 y * x
 149 
 150 % Note: x*y is not necessarily y*x!!!
 151 
 152 % Define new matrix
 153 z = [1 1; 2 2]
 154 
 155 % Works:
 156 y*z
 157 z*x
 158 
 159 % Doesn't work:
 160 z*y
 161 x*z
 162 
 163 %% Make your own matrices
 164 
 165 % Identity matrix
 166 id = eye(3)
 167 
 168 % Example:
 169 x*id
 170 
 171 id*x'
 172 
 173 % diagonal matrix
 174 di = eye(3)
 175 di(1,1) = 1
 176 di(2,2) = 2
 177 di(3,3) = 3
 178 
 179 % Multiplies columns by a factor:
 180 x*di
 181 
 182 % Multiplies rows by a factor
 183 di*y
 184 
 185 %% Some useful functions
 186 
 187 % sum/average across columns of a matrix
 188 % note: most Matlab function operate column-by-column
 189 sum( x )
 190 mean( x )
 191 
 192 % sum across rows of a matrix
 193 sum( x' )
 194 mean( x' )
 195 
 196 % get the diagonal of a (square) matrix
 197 mydiag = diag(di)
 198 
 199 % dimensions of a matrix, size()
 200 [m,n] = size(x)
 201 
 202 % dimension of a vector
 203 diaglen = length(mydiag)
 204 
 205 % create a matrix/vector with ones
 206 ones(10)   % creates 10x10 matrix
 207 ones(10,1) % creates 10x1 column vector
 208 
 209 % create a matrix/vector with zeros
 210 zeros(10)   % creates 10x10 matrix
 211 zeros(1,10) % creates 1x10 row vector
 212 
 213 % create matrix/vector with standard uniform random numbers in interval 0-1
 214 rand(3)
 215 
 216 % create matrix/vector with standard normal random numbers in interval 0-1
 217 randn(3)
 218 
 219 % "reshaping" a matrix or a vector
 220 x = 1:10
 221 reshape(x,5,2)
 222 reshape(x,2,5)
 223 
 224 % Kronecker product ("concatenates" matrices/vectors)
 225 kron(id,y)