Difference between revisions of "Trace"
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== Properties == | == Properties == | ||
| − | Viewed as a function from <math>n \times n</math> matrices to the underlying [[field]] (frequently the [[real number]]s), the trace is a [[linear map]]: it is not difficult to verify that <math>\text{tr}(cA + B) = c\text{tr}(A) + \text{tr}(B)</math> for any <math>n \times n</math> matrices <math>A</math> and <math>B</math>. | + | Viewed as a function from <math>n \times n</math> matrices to the underlying [[field]] (frequently the [[real number]]s), the trace is a [[linear map]]: it is not difficult to verify that <math>\text{tr}(cA + B) = c\, \text{tr}(A) + \text{tr}(B)</math> for any <math>n \times n</math> matrices <math>A</math> and <math>B</math> and any scalar <math>c</math>. |
Latest revision as of 19:27, 2 March 2010
The trace of a square 
matrix is the sum of the elements of the main diagonal of the matrix. For example, the trace of the matrix 
is 
.
Properties
Viewed as a function from matrices to the underlying field (frequently the real numbers), the trace is a linear map: it is not difficult to verify that 
for any matrices 
and 
and any scalar 
.
See also
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