Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Mathematics and Algorithms > Matrices and Linear Algebra > Matrix Operations > Tr >
Mathematica > Mathematics and Algorithms > Graphs & Networks > Graph Programming > Matrices and Linear Algebra > Matrix Operations > Tr >
Mathematica > Visualization and Graphics > Graphs & Networks > Graph Programming > Matrices and Linear Algebra > Matrix Operations > Tr >
BUILT-IN MATHEMATICA SYMBOLTutorials »|See Also »|More About »

Tr

Tr[list]
finds the trace of the matrix or tensor list.
Tr
finds a generalized trace, combining terms with f instead of Plus.
Tr
goes down to level n in list.
MORE INFORMATION
  • Tr[list] sums the diagonal elements .
  • Tr works for rectangular as well as square matrices and tensors.
EXAMPLESCLOSE ALL
Basic Examples   (1)
The trace of a matrix is the sum of the diagonal elements:
The trace of a matrix is the sum of the diagonal elements:
In[1]:=
Click for copyable input
Out[1]=
Scope   (2)
Symbolic trace:
Trace of a numerical matrix:
Trace of a sparse matrix:
Generalizations & Extensions   (6)
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:
Applications   (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 :
Properties & Relations   (2)
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 :
New in 4 | Last modified in 5
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF