Glossary of Select MATLAB Commands

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Section A.1 Glossary of Select MATLAB Commands

Subsection A.1.1 Mathematical Operations

`+`	Addition. Type `help plus` for information.
`-`	Subtraction. Type `help minus` for information.
`*`	Scalar or matrix multiplication. Type `help mtimes` for information.
`/`	Scalar or right matrix division. Type `help slash` for information. For matrices, the command `A/B` is equivalent to `A*inv(B)`.
`^`	Scalar or matrix powers. Type `help mpower` for information.
`.*`	Element by element multiplication. Type `help times` for information.
`.^`	Element by element exponentiation. Type `help power` for information.
`./`	Element by element division.

Subsection A.1.2 Built-in Mathematical Constants

`eps`	Machine epsilon, i.e. approximately the computer’s floating point roundoff error.
`i`	\(\sqrt{-1}\text{.}\)
`Inf`	\(\infty\text{.}\)
`NaN`	Not a number. Indicates an invalid operation such as \(0/0\text{.}\)
`pi`	\(\pi = 3.14159 \ldots\text{.}\)

Subsection A.1.3 Built-in Mathematical Functions

`abs(x)`	Absolute value \(\|x\|\text{.}\)
`acos(x)`	Inverse cosine \(\arccos{x}\text{.}\)
`asin(x)`	Inverse sine \(\arcsin{x}\text{.}\)
`atan(x)`	Inverse tangent \(\arctan{x}\text{.}\)
`cos(x)`	Cosine \(\cos{x}\text{.}\)
`cosh(x)`	Hyperbolic cosine \(\cosh{x}\text{.}\)
`cot(x)`	Cotangent \(\cot{x}\text{.}\)
`exp(x)`	Exponential function \(e^{x} = \exp{x}\text{.}\)
`log(x)`	Natural logarithm \(\ln{x}= \log_{e}{x}\text{.}\)
`sec(x)`	Secant \(\sec{x}\text{.}\)
`sin(x)`	Sine \(\sin{x}\text{.}\)
`sinh(x)`	Hyperbolic sine \(\sinh{x}\text{.}\)
`sqrt(x)`	Square root \(\sqrt{x}\text{.}\)
`tan(x)`	Tangent \(\tan{x}\text{.}\)
`tanh(x)`	Hyperbolic tangent \(\tanh{x}\text{.}\)
`max`	Computes maximum of the rows of a matrix.
`mean`	Computes the average of the rows of a matrix.
`min`	Computes the minimum of the rows of a matrix.

Subsection A.1.4 Built-in Numerical Mathematical Operations

`fzero`	Tries to find a zero of the specified function near a starting point or on a specified interval.
`inline`	Define a function in the command window.
`ode113`	Numerical multiple step ODE solver.
`ode45`	Runga-Kutta 45 numerical ODE solver.
`quad`	Numerical integration using an adaptive Simpson’s rule.
`dblquad`	Double integration.
`triplequad`	Triple integration.

Subsection A.1.5 Built-in Symbolic Mathematical Operations

`collect`	Collects powers of the specified variable is a given symbolic expression.
`compose`	Composition of symbolic functions.
`diff`	Symbolic differentiation.
`double`	Displays double-precision representation of a symbolic expression.
`dsolve`	Symbolic ODE solver.
`expand`	Expands an algebraic expression.
`factor`	Factor a polynomial.
`int`	Symbolic integration; either definite or indefinite.
`limit`	Finds two-sided limit, if it exists.
`pretty`	Displays a symbolic expression in a nice format.
`simple`	Simplifies a symbolic expression.
`subs`	Substitutes for parts a a symbolic expression.
`sym` or `syms`	Create symbolic variables.
`symsum`	Performs a symbolic summation, possibly with infinitely many entries.
`taylor`	Gives a Taylor polynomial approximation of a given order at a specified point.

Subsection A.1.6 Graphics Commands

`contour`	Plots level curves of a function of two variables.
`contourf`	Filled contour plot.
`ezcontour`	Easy contour plot.
`loglog`	Creates a log-log plot.
`mesh`	Draws a mesh surface.
`meshgrid`	Creates arrays that can be used as inputs in graphics commands such as `contour`, `mesh`, `quiver`, and `surf`.
`ezmesh`	Easy mesh surface plot.
`plot`	Plots data vectors.
`ezplot`	Easy plot for symbolic functions.
`plot3`	Plots curves in 3-D.
`polar`	Plots in polar coordinates.
`quiver`	Plots a vector field.
`semilogy`	Semilog plot, with logarithmic scale along the vertical direction.
`surf`	Solid surface plot.
`trimesh`	Plot based on a triangulation
`trisurf`	Surface plot based on a triangulation

Subsection A.1.7 Special MATLAB Commands

`:`	Range operator, used for defining vectors and in loops. Type `help colon` for information.
`;`	Suppresses output. Also separates rows of a matrix.
`=`	Assigns the variable on the left hand side the value of the right hand side.
`ans`	The value of the most recent unassigned.
`cd`	Change directory.
`clear`	Clears all values and definitions of variables and functions. You may also use to clear only specified variables.
`diary`	Writes a transcript of a MATLAB session to a file.
`dir`	Lists the contents in the current working directory. Same as `ls`.
`help`
`inline`	Define an inline function.
`format`	Specifies output format, e.g. `format long`.
`load`	Load variables from a file.
`save`	Saves workspace variables to a file.

Subsection A.1.8 MATLAB Programming

`==`	Is equal?
`~=`	Is not equal?
`<`	Less than?
`>`	Greater than?
`<=`	Less than or equal?
`break`	Breaks out of a `for` or `while` loop.
`end`	Terminates an `if`, `for` or `while` statement.
`else`	Alternative in an `if` statement.
`error`	Displays and error message and ends execution of a program.
`for`	Repeats a block of commands a specified number of times.
`function`	First word in a function program.
`if`	Checks a condition before executing a block of statements.
`return`	Terminates execution of a program.
`warning`	Displays a warning message.
`while`	Repeats a block of commands as long as a condition is true.

Subsection A.1.9 Commands for Matrices and Linear Algebra

Matrix arithmetic:

`A = [ 1 3 -2 5 ; -1 -1 5 4 ; 0 1 -9 0]`	Manually enter a matrix.
`u = [ 1 2 3 4]'`
`A*u`
`B = [3 2 1; 7 6 5; 4 3 2]`
`B*A`	multiply \(B\) times \(A\text{.}\)
`2*A`	multiply a matrix by a scalar.
`A + A`	add matrices.
`A + 3`	add a number to every entry of a matrix.
`B.*B`	component-wise multiplication.
`B.^3`	component-wise exponentiation.

Special matrices:

`I = eye(3)`	identity matrix
`D = ones(5,5)`
`O = zeros(10,10)`
`C = rand(5,5)`	random matrix with uniform distribution in \([0,1]\text{.}\)
`C = randn(5,5)`	random matrix with normal distribution.
`hilb(6)`
`pascal(5)`

General matrix commands:

`size(C)`	gives the dimensions (\(m \times n\)) of \(A\text{.}\)
`norm(C)`	gives the norm of the matrix.
`det(C)`	the determinant of the matrix.
`max(C)`	the maximum of each row.
`min(C)`	the minimum in each row.
`sum(C)`	sums each row.
`mean(C)`	the average of each row.
`diag(C)`	just the diagonal elements.
`inv(C)`	inverse of the matrix.

Matrix decompositions:

`[L U P] = lu(C)`
`[Q R] = qr(C)`
`[U S V] = svd(C)`	singular value decomposition.