|
In mathematics, a matrix of ones or all-ones matrix is a matrix where every element is equal to one.〔.〕 Examples of standard notation are given below: : Some sources call the all-ones matrix the unit matrix, but that term may also refer to the identity matrix, a different matrix. ==Properties== For an ''n×n'' matrix of ones ''J'', the following properties hold: * The trace of ''J'' is ''n'',〔.〕 and the determinant is 1 if ''n'' is 1, or 0 otherwise. * The rank of ''J'' is 1 and the eigenvalues are ''n'' (once) and 0 (''n''-1 times).〔; , (p. 65 ).〕 * ''J'' is positive semi-definite matrix. This follows from the previous property. *〔.〕 *The matrix is idempotent. This is a simple corollary of the above.〔 * where exp(''J'') is the matrix exponential. * ''J'' is the neutral element of the Hadamard product.〔.〕 *If ''A'' is the adjacency matrix of a ''n''-vertex undirected graph ''G'', and ''J'' is the all-ones matrix of the same dimension, then ''G'' is a regular graph if and only if ''AJ'' = ''JA''.〔.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「matrix of ones」の詳細全文を読む スポンサード リンク
|