Matlab Fundamentals: Matrices

1. When we define a list using a command such as t=1:3, Matlab creates a row vector containing 3 elements.
2. A row vectors can be turned into a column vector using the transpose (') operator. Using the definition of t above, note what happens for the command t' and t''
3. The multiplication, division and exponential operators (*, /, ^) operating on two vectors will do matrix multiplications, not multiplying the elements together.
4. Given a list x=0:2:10; then x.*x or x.^2 will give a list with the squares of the even integers [0 4 16 36 64 100] because it is doing list or array multiplication
5. The command x*x will produce an error (since you can't do matrix multiplication of two row vectors together).
6. The command x*x' be will give the value of 220 (0+4+16+36+64+100=220) since the transpose operator (') means that we have a row times column matrix (resulting in a scalar).
7. The command x'*x will result in a 6 by 6 matrix
8. We can extract and modify elements of a list
• Selecting an element of a list, use x(3)
• We can set an element using x(3)=100;
• To select a range of a lixt, use x(3:5) or x(:3) or x(5:)

Two Dimensional Matrices and Three Dimensional Functions

1. A 3x3 matrix can be initialized using . y = zeros(3)
2. Using explicit references, e.g. A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
• Elements in each row are separated by spaces or commas
• Each row is separated by a semicolon or by pressing the return key
3. Array operations (+ - .* ./ .^) operate on each element of a matrix, For example, try A.^2 or A.*A
4. Matrix operations are (+ - * / ^), For example, try A^2 or A*A
5. We can extend two 1-D vectors to a 2-D matrix (which we can use for calculations) use meshgrid
6. For example, we can make a multiplication table using array multiplication
• x = 1:5
• y = 0:3
• [X Y] = meshgrid(x,y)
• B = X .* Y
7. Plot using mesh, surf, contour
8. Calculate and Plot sinc(R)=sin(R)/R using (MAKE SURE YOU USE .^ and ./)
• x = -16:1.1:16;
• [X Y] = meshgrid(x,x);
• R = sqrt(X.^2 + Y.^2);
• SincR = sin(R)./R;
• surf(X,Y,SincR)
• colorbar
9. You can select subranges of matrices, A(3,3) or A(1:2,1:2) or A(1:2,:) or A(:,2:3)

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   Electronic Copy: http://physics.gac.edu/~huber/matlab/mtlabmat.htm
   Revised: 28-JAN-97 by Tom Huber, Physics Department, Gustavus Adolphus College.