Table of Contents

Solve augmented matrix

Use A for the coefficient matrix and B for the augmented column:

>> A=[1 2 -3; 0 1 -3; -3 -5 7]

A =

     1     2    -3
     0     1    -3
    -3    -5     7

>> B=[-2; -5; 3]

B =

    -2
    -5
     3

>> c = linsolve(A,B)

c =

    2.0000
    1.0000
    2.0000

Return eigenvalues D and eigenvectors V

Where D represents \(\Lambda\) and V represents \(S\). Matlab seems to present the eigenvalues in ascending order and S columns will be sorted accordingly.

>> A=[.5 .4; -.104 1.1]

A =

    0.5000    0.4000
   -0.1040    1.1000

>> [V,D] = eig(A)

V =

   -0.9806   -0.6097
   -0.1961   -0.7926


D =

    0.5800         0
         0    1.0200

>>

Scale eigenvectors

  • Matlab will provide normalized eigenvectors that have magnitude 1 (sum the squares of all the entries in a column of a 2 by 2 matrix and you get 1). To “normalize” it in a way that the first entry row is 1 we can divide each vector by it’s first element, which is vectorized using bsxfun(@rdivide, V, V(1,:)). Hopefully we got rid of long decimals and can use the basic calculator to figure out whole number columns.

Transpose

B = transpose(A)
B = A.'

Vector length

n = norm(v)

Matrix multiplication

C = mtimes(A,B)
  • also works with just *

Matrix sum

S = sum(A)

Matlab comments

%{
   Comment
   block
%}
% comment line

Inverse matrix

S=inv(A)
%or
S=A^(-1)

Identity Matrix

I = eye(n) %returns an n-by-n identity matrix with ones on the main diagonal and zeros elsewhere.
I = eye(n,m) %returns an n-by-m matrix with ones on the main diagonal and zeros elsewhere.

Zero matrix

O = zeros(n) %returns an n-by-n matrix of zeros.
O = zeros(n,m) %returns an n-by-m matrix of zeros.

Row reduced echelon form

R = rref(A) %returns the reduced row echelon form of A using Gauss-Jordan elimination with partial pivoting.

Normalize columns of matrix

N=normc(M) %normalizes the columns of M to a length of 1.