Difference between MATLAB's matrix notations

Question

How do you read the following MATLAB codes?

#1

K>> [p,d]=eig(A)                     // Not sure about the syntax.

p =

    0.5257   -0.8507
   -0.8507   -0.5257


d =                               // Why do you get a matrix?

    0.3820         0                  
         0    2.6180

#2

K>> p,d=eig(A)                  // Not sure about the syntax.

p =

    0.5257   -0.8507
   -0.8507   -0.5257


d =                                       // Why do you get a vector?

    0.3820
    2.6180

where

A =

     2     1
     1     1

Answer 1

In your second case p,d=eig(A) MATLAB is merely printing the previously calculated value of p from case 1 and then running the command d=eig(A).

Before running case 2 try

>> clear p d

If you then run p,d=eig(A) it will return an error saying that p is undefined function or variable.

From help eig:

E = EIG(X) is a vector containing the eigenvalues of a square
matrix X.

[V,D] = EIG(X) produces a diagonal matrix D of eigenvalues and a
full matrix V whose columns are the corresponding eigenvectors so
that X*V = V*D.

Note there is no V,D = EIG(X) option. MATLAB functions that return more than one value will group them using the format:

[ ] = function()

Answer 2

p,d=eig(A)

is the same as

p
d=eig(A)