$tr(A) = ( A_11 + A_22 )$

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Trace of 2X2 Matrix

[Math | Numerical Analysis | Matrices] This equation computes the trace of a two-by-two matrix. Given a square matrix where

A = $[[A_11,A_12],[A_21,A_22]]$ ,

The Trace of this matrix is defined as tr (A) = $A_11$ + $A_22$

The trace can be used in a number of numerical analyses computing things like the eigenvalues of a matrix.

Notes

The trace of a square matrix (the matrix must be a square matrix) is simply the sum of the diagonals: $A_11 + A_22 +$ ... $A_nn$ .

Note that the trace of a matrix is equal to that of its transpose, i.e., tr(A) = tr(A^T)