Trace

Trace of ab

Trace of ab
  1. What is trace of AB?
  2. How do you find the trace of AB?
  3. Is trace of AB equal to trace of a trace of B?

What is trace of AB?

The trace of AB is the sum of diagonal entries of this matrix. By the definition of the product of two matrices, these entries are: A(1,1)B(1,1)+A(1,2)B(2,1)+...+A(1,n)B(n,1), A(2,1)B(1,2)+A(2,2)B(2,2)+...+A(2,n)B(n,2), ..........................................

How do you find the trace of AB?

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.

Is trace of AB equal to trace of a trace of B?

That is, each element of B is multiplied by its transpose element of A. The sum of all these is, by definition, Tr(BA). Thus the two traces are equal.

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