'Rank' function

I am wondering what is the output of 'rank' function in Matlab: For example:

>> A=[1 2 1 4; 2 3 1 3; 3 2 1 2; 4 3 1 1] A = 1 2 1 4 2 3 1 3 3 2 1 2 4 3 1 1 >> rank(A) ans = 3

and

>> rank(A(:,[1 2 3])) ans = 3

but

>> rank(A(:,[1 2 4])) ans = 3

and

>> rank(A(:,[1 3 4])) ans = 2

and

>> rank(A(:,[2 3 4])) ans = 3

Thanks in advance if someone tell me what are the output numbers?

Answer 1

[Thomas]

doc rank

The rank function provides an estimate of the number of linearly independent rows or columns of a full matrix.

k = rank(A) returns the number of singular values of A that are larger than the default tolerance, max(size(A))*eps(norm(A)).

k = rank(A,tol) returns the number of singular values of A that are larger than tol

Answer 2

[Ahmad Karnama]

Thanks Thomas! I read this on the website and matlab help but I am wondering it it estimated the linearly independent 'rows' or 'columns'?? and how can you interpret the results I am getting? Regards, Ahmad

[Thomas]

A

A =

1.00 2.00 1.00 4.00

2.00 3.00 1.00 3.00

3.00 2.00 1.00 2.00

4.00 3.00 1.00 1.00

>> A(:,[2 3 4])

ans =

2.00 1.00 4.00

3.00 1.00 3.00

2.00 1.00 2.00

3.00 1.00 1.00

>> A(:,[1 2 3])

ans =

1.00 2.00 1.00

2.00 3.00 1.00

3.00 2.00 1.00

4.00 3.00 1.00

>> rank(A(:,[1 2 3]))

ans =

3.00

A(:,[1 2 3]) gives a new matrix with col 1,2 and 3 from A

and

rank(A(:,[1 2 3]))

ans =

3.00

gives the rank of this new matrix..

Answer 3

[Jan]

A = [1 2 1 4; 2 3 1 3; 3 2 1 2; 4 3 1 1]
rank(A) ans = 3

This means, that A has 3 independend rows or columns.

rank(A(:,[1 2 3])) ans = 3

The first three columns are independent.

rank(A(:,[1 2 4])) ans = 3

The columns 1,2,3 are also independent.

rank(A(:,[1 3 4])) ans = 2

One vector of this set is a linear combination of the two others.

rank(A(:,[2 3 4])) ans = 3

These three columns are independent again.

This is only the application of the definition Thomas has given already. Therefore I do not understand the problem.