BUILT-IN MATHEMATICA SYMBOL

Tr

Tr[list]
finds the trace of the matrix or tensor list.

finds a generalized trace, combining terms with f instead of Plus.

goes down to level n in list.

The trace of a matrix is the sum of the diagonal elements:

Out[1]=

Symbolic trace:

Trace of a numerical matrix:

Trace of a sparse matrix:

For a vector Tr gives the sum of the elements:

For a higher-rank tensor, Tr gives the sum of elements with equal indices:

Apply a function to the diagonal elements of a matrix:

Extract the diagonal of a matrix as a list:

Only consider down to level 1; this adds the rows of the matrix:

Only consider down to level 2:

Find the determinant of a triangular matrix:

Define an inner product for the cone of positive definite matrices using

:

Project the matrix

onto the space spanned by the matrix

:

The trace of a matrix is invariant under similarity transformations:

The invariance means that the sum of the eigenvalues must equal the trace:

The Frobenius norm is defined as

: