MATLAB Brief List of Commands

NOTE: Command syntax is case-sensitive!

Basic commands for variables and files

    matlab    loads the program matlab into your workspace.
    quit      quits matlab, returning you to the operating system.
    exit      same as quit.
    who       lists all of the variables in your matlab workspace.
    whos      list the variables and describes their matrix size.
    clear     deletes all matrices from active workspace.
    clear x   deletes the matrix  x  from active workspace.
    ...       the ellipsis defining a line continuation is three
              successive periods.
    save      saves all the matrices defined in the current     
              session into the file, matlab.mat.
    load      loads contents of matlab.mat into current workspace.
    save filename  saves the contents of workspace into 
                   filename.mat
    save filename x y z
              saves the matrices x, y and z into the file titled
              filename.mat.
    load filename  loads the contents of filename into current
                   workspace; the file can be a binary (.mat) file
                   or an ASCII file.
    !         the ! preceding any unix command causes the unix
              command to be executed from matlab.

SPECIAL MATRICES

    zeros(n)  creates an nxn matrix whose elements are zero.
    zeros(m,n)   creates a  m-row, n-column matrix of zeros.
    ones(n)   creates a n x n square matrix whose elements are 1's
    ones(m,n)' creates a mxn matrix whose elements are 1's.
    ones(A)   creates an m x n matrix of 1's, where m and n are 
              based on the size of an existing matrix, A. 
    zeros(A)  creates an mxn matrix of 0's, where m and n are
              based on the size of the existing matrix, A.
    eye(n)    creates the nxn identity matrix with 1's on the
              diagonal.

ALGEBRAIC OPERATIONS IN MATLAB

Scalar Calculations

                        +         addition       
                        -         subtraction
                        *         multiplication
                        /         right division (a/b means a ÷ b)
                        \         left division  (a\b means b ÷ a)
                        ^         exponentiation

The precedence or order of the calculations included in a single line of code follows the below order:

         Precedence                Operation
              1         parentheses
              2         exponentiation, left to right
              3         multiplication and division, left  right
              4         addition and subtraction, left  right

Matrix Algebra

In matrix multiplication, the elements of the product, C, of two matrices A*B is calculated from

         Cij = ‘ (Aik * Bkj)   {summation over the double index k}

To form this sum, the number of columns of the first or left matrix (A) must be equal to the number of rows in the second or right matrix (B). The resulting product, matrix C, has an order for which the number of rows equals the number of rows of the first (left) matrix (A) and the product (C) has a number of columns equal to the number of columns in the second (right) matrix (B). It is clear that A*B IS NOT NECESSARILY EQUAL TO B*A!

The PRODUCT OF A SCALAR AND A MATRIX is a matrix in which every element of the matrix has been multiplied by the scalar.

Array Products

Sometimes it is desired to simply multiply or divide each element of an matrix by the corresponding element of another matrix. These are called 'array operations" in 'matlab'. Array or element-by-element operations are executed when the operator is preceded by a '.' (period). Thus

    a .* b    multiplies each element of a by the respective
              element of b
    a ./ b    divides each element of a by the respective element
              of b
    a .\ b    divides each element of b by the respective element
              of a
    a .^ b    raise each element of a by the respective b element

Hermitian Conjugate and Transpose of a Matrix

    x'        The Hermitian conjugate of a matrix is obtained by
              interchanging the rows and columns and by taking complex conjugate 
              of all matrix elements.

    x.'       The transpose of a matrix is obtained by
              interchanging the rows and columns.

Inner (or dot or scalar) Product of Two Vectors

The inner product of two row vectors G1 and G2 is

G1*G2'
    

The inner product of two column vectors H and J is

H'*J

Outer Product of Two Vectors

If two row vectors exist, G1 and G2, the outer product is simply

    G1' * G2       Note: G1' is nx1 and G2 is 1xn

and the result is a square matrix in contrast to the scalar result for the inner product. DON'T CONFUSE THE OUTER PRODUCT WITH THE VECTOR PRODUCT IN MECHANICS! If the two vectors are column vectors, the outer product must be formed by the product of one vector times the transpose of the second!

Solution to Simultaneous Equations

Using the Matrix Inverse

    inv(a)    returns the inverse of the matrix  a.
              If ax=b is a matrix equation and  a  is the
              coefficient matrix, the solution  x  is  x=inv(a)*b.

Using Back Substitution

    a\b       returns a column vector solution for the matrix
              equation  ax=b where a is a coefficient matrix.
    b/a       returns a row vector solution for the matrix
              equation  xa=b where a is a coefficient matrix.

Commands involving functions

    inline    define a function, e.g.  f = inline('x^2')
    fplot     generate the graph of a function, e.g. fplot(f,[a,b])
              plots f (a string defn) over the interval [a,b]
    fzero     find the zero of a function, e.g.  fzero(f,x0), 
              computes zero of f near x0 or if x0 a vector then
              in the interval [x0_1, x0_2].

Commands useful for plotting

    plot(x,y) creates an Cartesian plot of the vectors x & y.
    plot(y)   creates a plot of y vs. the numerical values of the
              elements in the y-vector.
    semilogx(x,y) plots log(x) vs y.
    semilogy(x,y)  plots x vs log(y)
    loglog(x,y)    plots log(x) vs log(y).
    grid      creates a grid on the graphics plot.
    title('text')  places a title at top of graphics plot.
    xlabel('text') writes 'text' beneath the x-axis of a plot.
    ylabel('text') writes 'text' beside the y-axis of a plot.
    text(x,y,'text')    writes 'text' at the location (x,y) .
    text(x,y,'text','sc') writes 'text' at point x,y assuming
                        lower left corner is (0,0) and upper
                        right corner is (1,1).
    gtext('text') writes text according to placement of mouse
    hold on   maintains the current plot in the graphics window
              while executing subsequent plotting     commands.
    hold off  turns OFF the 'hold on' option.
    polar(theta,r) creates a polar plot of the vectors r & theta
                   where theta is in radians.
    bar(x)    creates a bar graph of the vector x. (Note also
              the command stairs(y).)

    bar(x,y)  creates a bar-graph of the elements of the vector y,
              locating the bars according to the vector elements
              of 'x'. (Note also the command stairs(x,y).)
    hist(x)   creates a histogram. This differs from the bargraph
              in that frequency is plotted on the vertical axis.
    mesh(z)   creates a surface in xyz space where z is a matrix
              of the values of the function z(x,y). z can be
              interpreted to be the height of the surface above
              some xy reference plane.
    surf(z)   similar to mesh(z), only surface elements depict
              the surface rather than a mesh grid.
    contour(z)     draws a contour map in xy space of the function
                   or surface z.
    meshc(z)  draws the surface z with a contour plot beneath it.
    meshgrid  [X,Y]=meshgrid(x,y) transforms the domain specified
              by vectors x and y into arrays X and Y that can be
              used in evaluating functions for 3D mesh/surf plots.
    print     sends the contents of graphics window to printer.
    print filename -dps      writes the contents of current
              graphics to 'filename' in postscript format.

Equation Fitting

    polyfit(x,y,n) returns the coefficients of the n-degree
         polynomial for the vectors x and y. n must be at least 1
         larger than the length of the vectors x and y. If n+1 =
         length(x) the result is an interpolating polynomial. If
         n+1 > length(x) the result is a least-squares polynomial
         fit. The coefficients are stored in order with that of
         the highest order term first and the lowest order last.
    polyval(c,x)   calculates the values of the polynomial whose
         coefficients are stored in  c, calculating for every
         value of the vector x.

Data Analysis Commands

    max(x)    returns the maximum value of the elements in a
              vector or if x is a matrix, returns a row vector
              whose elements are the maximum values from each
              respective column of the matrix.
    min (x)   returns the minimum of x (see max(x) for details).
    mean(x)   returns the mean value of the elements of a vector
              or if x is a matrix, returns a row vector whose
              elements are the mean value of the elements from
              each column of the matrix.
    median(x) same as mean(x), only returns the median value.
    sum(x)    returns the sum of the elements of a vector or if x
              is a matrix, returns the sum of the elements from
              each respective column of the matrix.
    prod(x)   same as sum(x), only returns the product of
              elements.
    std(x)    returns the standard deviation of the elements of a
              vector or if x is a matrix, a row vector whose
              elements are the standard deviations of each
              column of the matrix.
    sort(x)   sorts the values in the vector x or the columns of
              a matrix and places them in ascending order. Note
              that this command will destroy any association that
              may exist between the elements in a row of matrix x.
    hist(x)   plots a histogram of the elements of vector, x. Ten
              bins are scaled based on the max and min values.
    hist(x,n) plots a histogram with 'n' bins scaled between the
              max and min values of the elements.
    hist((x(:,2))  plots a histogram of the elements of the 2nd
                   column from the matrix x.
    fliplr(x) reverses the order of a vector. If x is a matrix,
              this reverse the order of the columns in the matrix.
    flipud(x) reverses the order of a matrix in the sense of
              exchanging or reversing the order of the matrix
              rows. This will not reverse a row vector!
    reshape(A,m,n)      reshapes the matrix A into an mxn matrix
              from element (1,1) working column-wise.

Miscellaneous Commands

    length(x) returns the number elements in a vector.
    size(x)   returns the size m(rows) and n(columns) of matrix x.
    rand      returns a random number between 0 and 1.
    randn     returns a random number selected from a normal
              distribution with a mean of 0 and variance of 1.
    rand(A)   returns a matrix of size A of random numbers.