Relation between the matrix trace and the amplitude of each element

1. What does the trace of a matrix tell you?
2. Is trace of AB equal to trace of BA?
3. What is the trace of a 2x2 matrix?

What does the trace of a matrix tell you?

Definition 1

The trace of a matrix A, designated by tr(A), is the sum of the elements on the main diagonal.

Is trace of AB equal to trace of BA?

The trace is only defined for a square matrix (n × n). It can be proved that the trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities). It can also be proved that tr(AB) = tr(BA) for any two matrices A and B.

What is the trace of a 2x2 matrix?

So to find the inverse of a 2x2 matrix, interchange the diagonal elements, change the sign of the off-diagonal elements, and divide by the determinant. where Tr(A) = a + d is the trace of A. (The trace of a square matrix is the sum of the diagonal elements.)