For what matrices are generalized inverses A+ of matrices defined? For only Finite dimensional or both finite and infinite dim'l, i.e. dimension does not matter?(adsbygoogle = window.adsbygoogle || []).push({});

If generalized inverses are defined for infinite dim'l matrices, then I have a trouble in Penrose's proof for the existence of generalized inverses of matrices in 1955: (Penrose,1955) (A*A), (A*A)^2, (A*A)^3,... CANNOT BE LINEARLY INDEPENDENT.

Trouble: For finite dimensional mxn matrices, I okey (A*A), (A*A)^2, (A*A)^3,... are linearly dependent since the dimension of vectore space of all mxn matrices are mn. This is a stopping reason for that sequence.

But, how can we say that (A*A), (A*A)^2, (A*A)^3,... are linearly dependent in the infinite dimensional case as well? I cannot see any stopping reason here. I looked Penrose's proof (of 1955), but there, Penrose did not write any restrictive words about dim of matrices to only finite dimensional case.

Note: I attached the Penrose's 1955 original proof as well.

**Physics Forums - The Fusion of Science and Community**

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

# The dimension for Generalized Inverses of matrices and Penrose's troubled proof

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - dimension Generalized Inverses | Date |
---|---|

A What separates Hilbert space from other spaces? | Jan 15, 2018 |

I ##SU(2)## generators in ##1##, ##2## and ##3## dimensions | Mar 16, 2017 |

I Angle between two vectors with many dimensions | Feb 3, 2017 |

A Modular forms, dimension and basis confusion, weight mod 1 | Nov 23, 2016 |

A For finite dimension vector spaces, all norms are equivalent | Sep 29, 2016 |

**Physics Forums - The Fusion of Science and Community**