Thank you mfb!mfb said:I think you answered your own question, but a quick look at Wikipedia would lead to the same result.
Trixie Mattel said:Hello,
Just wondering if the trace of a matrix is independent of basis, seeing as the trace of a matrix is equal to the sun of the eigenvalues of the operator that the matrix is a representation of.
Thank you
The trace of a matrix is the sum of the elements on the main diagonal, from the upper left corner to the lower right corner.
The trace is important because it is a measure of the sum of the eigenvalues of a matrix, which provides useful information about the matrix's properties and behavior.
Yes, the trace of a matrix is always a scalar value, regardless of the size or dimensions of the matrix.
The trace of a matrix is independent of basis, meaning it remains the same regardless of the basis used to represent the matrix. This is because the trace is a property of the matrix itself, not the basis used to represent it.
Yes, the trace of a matrix can be negative. It is simply the sum of the elements on the main diagonal, so it can be positive, negative, or zero depending on the values in the matrix.