ajayguhan said:Homework Statement
Let P be 2x2 complex matrice such that trace(p)=1 det(p)=-6 then trace(p^4-p^3) equals what...?
Homework Equations
Is there any formula for trace(A^n)
The Attempt at a Solution
Let the two eigen values be a,b
a+b=1 a*b= -6 solving we get a=(1+i√23)/2 and b =(1-i√23)/2
Trace(p^4-p^3)=trace(p^4)-trace(p^3)
A complex matrix is a matrix whose elements are complex numbers. A complex number is a combination of a real number and an imaginary number, written in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).
The trace of a complex matrix is the sum of the elements on the main diagonal of the matrix. In other words, it is the sum of the eigenvalues of the matrix.
The trace of a complex matrix can be calculated by adding the real parts of the eigenvalues of the matrix. Alternatively, it can be calculated by adding the elements on the main diagonal of the matrix.
The trace of a complex matrix is an important property as it is invariant under similarity transformations, meaning that it remains the same regardless of how the matrix is transformed. This makes it useful in a variety of mathematical applications.
The trace of a complex matrix can be used to calculate the determinant of the matrix, which is an important property in solving systems of linear equations. It is also used in the study of quantum mechanics and other areas of physics and engineering.