From chemistry-request@ccl.net Mon Jun 6 04:10:32 2005 Received: from yangtze.hku.hk (yangtze.hku.hk [147.8.148.244]) by server.ccl.net (8.13.1/8.13.1) with ESMTP id j568ATJq015184 for ; Mon, 6 Jun 2005 04:10:30 -0400 Received: from yangtze.hku.hk (localhost.localdomain [127.0.0.1]) by yangtze.hku.hk (8.13.1/8.13.1) with ESMTP id j566UmEg007110 for ; Mon, 6 Jun 2005 14:30:48 +0800 Received: from localhost (yamcy@localhost) by yangtze.hku.hk (8.13.1/8.13.1/Submit) with ESMTP id j566UljQ007107 for ; Mon, 6 Jun 2005 14:30:48 +0800 Date: Mon, 6 Jun 2005 14:30:47 +0800 (HKT) From: ChiYung Yam To: chemistry^at^ccl.net Subject: Pseudo-Hermiticity Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=failed version=3.0.3 X-Spam-Checker-Version: SpamAssassin 3.0.3 (2005-04-27) on server.ccl.net Dear all, I found from the literature that a matrix will have all real eigenvalues if it is pseudo-hermitian. For pseudo-hermitian, it means \etta A \etta^{-1} = A^{daggar} where \etta is a hermitian and invertible matrix and A is the matrix we are interested in. However, if given a matrix with complex eigenvalues, how can I make it pseudo-hermitian with minimal changes to the matrix elements? Is there any simple way to do it? Thank you very much Best regards, Yam