完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.author | 潘淑真 | en_US |
dc.contributor.author | Shu-Chen Pan | en_US |
dc.contributor.author | 吳培元 | en_US |
dc.contributor.author | Pei Yuan Wu | en_US |
dc.date.accessioned | 2014-12-12T02:31:28Z | - |
dc.date.available | 2014-12-12T02:31:28Z | - |
dc.date.issued | 2002 | en_US |
dc.identifier.uri | http://140.113.39.130/cdrfb3/record/nctu/#NT910507006 | en_US |
dc.identifier.uri | http://hdl.handle.net/11536/70939 | - |
dc.description.abstract | 在本論文中,我們探討有關矩陣交換子的性質,以及兩個矩陣的commutant的維數性質。 首先,讓A是個 n-by-n矩陣,我們証明出以下二件事是對等的,(a) A的每一個特徵值的幾何重數,不是等於1,就是等於它的代數重數。(b) 給任意的n-by-n矩陣B,如果A跟B的交換子C=AB-BA即跟A互換,又跟B 互換,則這樣的C必為零。 接下來,讓A和B是兩個n-by-n的可互換矩陣,我們証明出,如果相對於A的每一個特徵值,均有不超過兩個的Jordan block,或是每一個Jordan block 都是1-by-1的,則A和B的commutant的維數至少會是n。此外,我們也完整的指出何時等號會成立。譬如當A是nonderogatory 時,就是一個例子。 | zh_TW |
dc.description.abstract | In this thesis, we study properties of matrix commutators and the dimension of the commutant of two commuting matrices. First, we show that the following are equivalent conditions on a matrix A 2 Mn : (a) The geometric multiplicity of each eigenvalue of A is either equal to 1 or equal to its algebraic multiplicity. (b) For any B 2 Mn(C); if commutator C = AB ¡ BA commutes with both A and B, then C must be zero. Next, let A be an n-by-n complex matrix. If every eigenvalue of A has no more than two Jordan blocks or is associated with only 1-by-1 Jordan blocks, then for any B commutes with A, the dimension of the commutant of A and B is at least n. Moreover, under this condition on A we also completely determine when the above dimension equals n. In particular, this is the case when A is nonderogatory. | en_US |
dc.language.iso | zh_TW | en_US |
dc.subject | 交換子 | zh_TW |
dc.subject | 交換矩陣 | zh_TW |
dc.subject | 交換 | zh_TW |
dc.subject | Commutator | en_US |
dc.subject | Commutant | en_US |
dc.subject | commute | en_US |
dc.title | 交換子與交換矩陣 | zh_TW |
dc.title | Commutator and Commutant | en_US |
dc.type | Thesis | en_US |
dc.contributor.department | 應用數學系所 | zh_TW |
顯示於類別: | 畢業論文 |