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In linear algebra, the trace of an ''n''-by-''n'' square matrix ''A'' is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of ''A'', i.e., : where ''ann'' denotes the entry on the ''n''-th row and ''n''-th column of ''A''. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis. This characterization can be used to define the trace of a linear operator in general. Note that the trace is only defined for a square matrix (i.e., ). The trace is related to the derivative of the determinant (see Jacobi's formula). The term trace is a calque from the German ''Spur'' (cognate with the English ''spoor''), which, as a function in mathematics, is often abbreviated to "tr". == Example == Let ''A'' be a matrix, with :. Then :. 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「Trace (linear algebra)」の詳細全文を読む スポンサード リンク
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