Matrix Input and Access

This section familiarises you with basic commands to input matrices/vectors and accessing their elements. You should memorise these to speed up your coding.

Basic syntax

To try out the commands on this page just type them directly into the MATLAB Command Window and hit <Enter> to execute them.

Most MATLAB commands follow one of the following syntaxes

variable = expression;
variable = command(arguments);
variable = command(arguments)
command(arguments)

The semicolon at the end of a command ; suppresses the display of the result or the output of the command. Lines can be commented out by starting the line with a percentage sign %.

% this is a comment which will not be executed
command(arguments)

Variables

In MATLAB, we store any kind of data (numbers, strings etc.) in variables. Here are a few examples of how to assign variables.

x = 1                       % store scalar value
y = 3 + 2 * exp(x);         % evaluate expression and store value
z = 3 + 2 * exp(x)          % evaluate expression, store and print value

y                           % print value to console
display(y)                  % equivalent

u = 'I am not a number'     % store strings

Vectors and matrices

Vectors and matrices are a special type of variables which can be created, accessed and modified using special commands.

Creating vectors and matrices

We can create row and column vectors either by entering them directly or by transposing vectors.

a = [1, 2, 3, 4, 5]         % row vector
b = [6; 7; 8; 9; 10]        % column vector

z = a'                      % column vector by transposing row vector
u = b'                      % row vector by transposing column vector

We can create matrices in a similar fashion by entering them row by row or by concatenating previously entered vectors or matrices.

A = [1, 2; 3, 4]            % declare matrix directly by rows

b = [5; 6];
B = [A, b]                  % join columns of 2x2 matrix A and 2x1 vector b
C = [A; b']                 % join rows of 2x2 matrix A and 1x2 vector b'

Accessing matrix and vector elements

We can access elements of a vector by supplying the indices of the values that we want to select in parentheses.

a = [5, 6, 7, 8, 9];        % row vector
b = a';                     % column vector

a(4)                        % returns the 4-th element
a(2:4)                      % returns elements 2-4 of row-vector
a([1, 3, 4])                % returns elements 1, 3, 4 of row-vector
a([1; 3; 4])                % equivalent

b([1, 3, 4])                % returns elements 1, 3, 4 of column vector

We can access elements of a matrix in a similar fashion by supplying either the indices with respect to the column-wise index or by supplying row and column indices separately.

A = [1, 2, 3; 4, 5, 6; 7, 8, 9]

A(4:6)                      % returns elements 4-6 counting columnwise
A(2,3)                      % returns element in row 2, column 3
A(1:2, 2:3)                 % return submatrix with rows 1-2, columns 2-3
A([1, 3], [1, 2])           % return submatrix with rows 1, 3 and columns 1, 2

We can also use the colon-operator : to select all elements of a specific dimension.

A(2, :)                     % return second row of the matrix
A(:, 3)                     % return third row of the matrix
A(1:2, :)                   % return submatrix with first two rows

The concepts discussed in this section extend easily to arrays of higher dimensions that 2.

Replacing elements in matrices

We can use the tools from the last section to easily replace individual elements of a matrix or even sub-matrices.

A = [1, 2, 3; 4, 5, 6; 7, 8, 9]

A(2,3) = 10                 % replace element in row 2, column 3
A(1:2, 1:2) = zeros(2,2)    % replace upper left 2x2 submatrix
A(:, 1) = [0, 1, 2]'        % replace first column

Special vectors and matrices

MATLAB supplies you with a set of functions that allow to create vectors or matrices that have a special form. These functions are often useful to avoid unnecessary repetition of inputs.

linspace and : operator

The linspace command and the : operator allow to create row vectors of sequences that are linearly spaced. Consider first the : operator.

a = 2:5                     % sequence from 2 to 5 in increments of 1
b = 2:3:11                  % sequence from 2 to 11 in increments of 3
c = 0:0.2:1                 % sequence from 0 to 1 in increments of 0.2

The linspace(x1, x2, N) command generates a row vector containing a sequence of N linearly spaced points between x1 and x2. If N is omitted, it generates 100 points.

c = linspace(0, 1, 6)       % same as c above
d = linspace(2, 9, 3)       % sequence from 2 to 8 with 3 values

logspace

The logspace operators works the same way as the linspace operator, but it produces a sequence of uniformly spaced values in the log-10 space, i.e. logspace(x1, x2, N) generates N points between 10^x1 and 10^x2.

e = logspace(0, 2, 4)       % logarithmically spaced values between 1 and 100

zeros, ones, nan

These commands create matrices of the supplied dimensions which are filled with 0, 1 or missing values (nan = not a number).

A = zeros(2, 3)
B = ones(1, 4)
C = nan(2,2)

eye

eye(n) creates an identity matrix (i.e. a square matrix with ones on the main diagonal and zeros everywhere else) of dimension .

eye(3)

diag

If X is a matrix, diag(X), returns the column vector which extracts the main diagonal of the matrix X. If x is a vectors, diag(X) returns a square diagonal matrix which has the vector x on its main diagonal

X = [1, 2; 3, 4]
x = [2, 5];

diag(X)
diag(x)

repmat

repmat(A, M, N) replicates the vector/matrix A copy its rows M times and its columns N times.

A = repmat([1, 2, 3], 4, 1)         % copy row vector a 4 times along rows
B = repmat([1 ,2; 3, 4], 2, 2)      % copy matrix 2 times along each dimension

reshape

reshape transforms a matrix into an matrix and can be used if the number of elements does not change i.e. if . It can e.g. be used to convert a matrix into a vector or vice versa.

X = [1, 2, 3; 4, 5, 6]

reshape(X, 1, 6)        % reshape into 1x6 vector
reshape(X, 3, 2)        % reshape into 3x2 matrix

Note that for the reshape command, the elements retain their index in the matrix which is counted column-wise.