EQUALITY OF ROW AND COLUMN RANK (o'Neil's proof) Is there smt wrong?(adsbygoogle = window.adsbygoogle || []).push({});

http://www.mediafire.com/imageview.php?quickkey=znorkrmk3k1otjd&thumb=6

Theorem 7.9: EQUALITY OF ROW AND COLUMN RANK

Proof: Page 210.

It writes:....

so the dimension of this column space is AT MOST r (equal to r if these columns are linearly independent, less than r if they are not)

I THINK THIS IS WRONG. Look at the r vectors:

1 0

0 1

: 0

0 :

BETAr+1,1 BETAr+1,2

:

BETAm1 BETAm2

The first r columns of these r vectors are e1,e2,...er. Hence, they are DEFINITELY LINEARLY INDEPENDENT.

There is no way to obtain 1 in the first coordinate of the first of the r vectors from the remaining r-1 vectors since the 1st coordinate of all of the remaining r-1 vectors are all 0.

Hence, the correct one should be:

so the dimension of this column space is EXACTLY r.

Where am I wrong? or O'neil's is really wrong as I indicated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# EQUALITY OF ROW AND COLUMN RANK (O'Neil's proof) Is there smt wrong?

Loading...

Similar Threads for EQUALITY COLUMN RANK |
---|

I Geometric intuition of a rank formula |

I Can a shear operation introduce a new linear dependency? |

**Physics Forums | Science Articles, Homework Help, Discussion**