%%% matrices.m: to run this script noninteractively, type
%%% matlab < manipul.m > manipul.out
%%%
%%% will dump output into file manipul.out
%%%
%%% contains some examples of array and matrix manipulation

%% Cleanup the environment a bit
clear variables;
clc;
echo on

x = [1.0 2 3.0]
A = [4.0 5.0 7.0; 8.1 6.2 1.2]
A = [A ; x]

%% Inverse of A
inv(A)

%% Transpose of matrix
B = A'

%% Sum of matrices
C = A + B

%% Matrix Products
C = A*B
y = C*x'

%% Matrix Factorining
[L U] = lu(A)
[Q R] = qr(A)

%% Eigenvalues computed two different ways
%% Poly uses an unusual algorithm - see the reference manual
eig(A)
roots(poly(A))

%% V = Eigenvectors, D = Eigenvalues
[V D] = eig(A)

%% Matlab checks for ill conditioned problems
%% e.g. inverse of Hilbert matrix
inv(hilb(12))

cond(hilb(12))

%% The dot product, computed two different ways
y*x	%% row * column
dot(x,y)

%% The product of a column vector with a row vector gives a matrix
y * x

%% The cross product
cross(x,y)

%% Normalize a vector in the Frobenious norm
x / norm(x, 'fro')

%% Normalize a vector in the Lpi norm
x / norm(x, pi)