trace of a matrix
Let be a square matrix of order . The trace of the matrix is the sum of the main diagonal:
The trace of a matrix is also commonly denoted as or .
If and are matrices such that is a square matrix, then
For this reason it is possible to define the trace of a linear transformation, as the choice of basis does not affect the trace. Thus, if are matrices such that is a square matrix, then
See the proof of properties of trace of a matrix.
- 1 The Trace of a Square Matrix. Paul Ehrlich, [online] http://www.math.ufl.edu/ ehrlich/trace.htmlhttp://www.math.ufl.edu/ ehrlich/trace.html
- 2 Z.P. Yang, X.X. Feng, A note on the trace inequality for products of Hermitian matrix power, Journal of Inequalities in Pure and Applied Mathematics, Volume 3, Issue 5, 2002, Article 78, http://www.emis.de/journals/JIPAM/v3n5/082_02.htmlonline.
|Title||trace of a matrix|
|Date of creation||2013-03-22 11:59:56|
|Last modified on||2013-03-22 11:59:56|
|Last modified by||Daume (40)|