Geology Reference
In-Depth Information
APPENDIX A
In linear algebra, the trace of a (n×n) square matrix A is defined to be the sum of the diagonal elements.
a
.
.
.
a
11
1
n
a
a
a
21
22
2
n
A
=
.
.
.
.
a
.
.
a
n
1
nn
n
trace
( )
=
∑
a
+
a
+ +
...
a
=
a
11
22
nn
ii
i
=
1
where a
ii
represents the entry on the ith row and ith column of A. Equivalently, the trace of a matrix is
the sum of its eigenvalues, making it an invariant with respect to a change of basis. This characterization
can be used to define the trace for a linear operator in general. The trace is only defined for a square
matrix (n×n). Geometrically, the trace can be interpreted as the infinitesimal change in volume, as the
derivative of the determinant, which is made precise in Jacobi's formula.
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