x = Z\z

[oort]

Hello.

If x = Z\z is the solution of Zx=z and only square systems have solution
then why the operation of non-square matrices Z gives "numerical values"?
Don't you think that it should give some error message? 

For instance:

octave:1> A = [3, 2, 6; 2, -2, 1; -1, 0.5, 3]
A =

   3.00000   2.00000   6.00000
   2.00000  -2.00000   1.00000
  -1.00000   0.50000   3.00000

octave:2> a = [1; 2; 3]
a =

   1
   2
   3

octave:3> A\a
ans =

  -0.74684
  -1.26582
   0.96203

OK... "A" is a 3x3 matrice and "a" is a 3x1 matrice 

But:

octave:4> B = [3, 2; 2, -2; -1, 0.5]
B =

   3.00000   2.00000
   2.00000  -2.00000
  -1.00000   0.50000

octave:5> b = [1; 2; 3]
b =

   1
   2
   3

octave:6> B\b
ans =

   0.29801
  -0.11479

Now we have a system of 3 equations and 2 variables. It's a overdefined
system. Curiously B*x does not give equal to "b"...


And if we use a underdefined system we aldo reach a "numeric" result.

octave:7> C = [3, 2, 6; 2, -2, 1]
C =

   3   2   6
   2  -2   1

octave:8> c = [1; 2]
c =

   1
   2

octave:9> C\c
ans =

   0.42175
  -0.51459
   0.12732

How it is possible to have a "result" from a underdifined system?
Curiously  if we put a third row with zeros in C and if we calculate C*x we
obtain "c". However in octave x = [0.42175; -0.51459; 0.12732] and in MATLAB
x = [0; -0.7857; 0.4286] 
-- 
View this message in context: 
http://octave.1599824.n4.nabble.com/x-Z-z-tp3178365p3178365.html
Sent from the Octave - General mailing list archive at Nabble.com.