save 'file.mat' - save variables to file.mat
load 'file.mat' - load variables from file.mat
diary on - record input/output to file diary
diary off -stop recording
whos - list all variables currenly defined
clear - delete/undefine all variables
help - command quick help on a given command
doc command - extensive help on a given command

x = 3 define variable x to be 3
x = [1 2 3] set x to the 1×3 row-vector (1,2,3)
x = [1 2 3]; same, but don't echo x to output
x = [1;2;3] set x to the 3×1 column-vector (1,2,3)
A = [1 2 3 4;5 6 7 8;9 10 11 12]; set A to the 3×4 matrix with rows 1,2,3,4 etc.
x(2) = 7 change x from (1,2,3) to (1,7,3)
A(2,1) = 0 change A2,1 from 5 to 0

34, 7+4, 2-6 8/3 multiply, add, subtract, and divide numbers
3^7, 3^(8+2i) compute 3 to the 7th power, or 3 to the 8+2i power
sqrt(-5) compute the square root of –5
exp(12) compute e12
log(3), log10(100) compute the natural log (ln) and base-10 log (log10)
abs(-5) compute the absolute value |–5| sin(5pi/3) compute the sine of 5π/3
besselj(2,6) compute the Bessel function J2(6)

x * 3 multiply every element of x by 3
x + 2 add 2 to every element of x
x + y element-wise addition of two vectors x and y
A * y product of a matrix A and a vector y
A * B product of two matrices A and B
x * y not allowed if x and y are two column vectors!
x .* y element-wise product of vectors x and y
A^3 the square matrix A to the 3rd power x^3 not allowed if x is not a square matrix!
x.^3 every element of x is taken to the 3rd power
cos(x) the cosine of every element of x
abs(A) the absolute value of every element of A
exp(A) e to the power of every element of A
sqrt(A) the square root of every element of A
expm(A) the matrix exponential eA
sqrtm(A) the matrix whose square is A

x.', A.' the transposes of x and A
x', A' the complex-conjugate of the transposes of x and A
x' * y the dot (inner) product of two column vectors x and y

rand(12,4) a 12×4 matrix with uniform random numbers in [0,1)

x(2:12) the 2nd to the 12th elements of x
x(2:end) the 2nd to the last elements of x
x(1:3:end) every third element of x, from 1st to the last
x(:) all the elements of x
A(5,:) the row vector of every element in the 5th row of A
A(5,1:3) the row vector of the first 3 elements in the 5th row of A
A(:,2) the column vector of every element in the 2nd column of A
diag(A) column vector of the diagonal elements of A

A \ b for A a matrix and b a column vector, the solution x to Ax=b
inv(A) the inverse matrix A–1
[L,U,P] = lu(A) the LU factorization PA=LU
eig(A) the eigenvalues of A
[V,D] = eig(A) the columns of V are the eigenvectors of A, and the diagonals diag(D) are the eigenvalues of A

plot(y) plot y as the y axis, with 1,2,3,… as the x axis
plot(x,y) plot y versus x (must have same length)
plot(x,A) plot columns of A versus x (must have same # rows)
loglog(x,y) plot y versus x on a log-log scale semilogx(x,y) plot y versus x with x on a log scale semilogy(x,y) plot y versus x with y on a log scale
title('A Title') add a title A Title at the top of the plot xlabel('blah') label the x axis as blah
ylabel('blah') label the y axis as blah
legend('foo','bar') label 2 curves in the plot foo and bar
grid include a grid in the plot
figure open up a new figure window