- #1
samspotting
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If a matrix is diagonalizable, how does its trace equal the sum of its eigenvalues?
I can't find a proof for this anywhere.
I can't find a proof for this anywhere.
The trace of a matrix is the sum of the elements on its main diagonal. In other words, it is the sum of the values in the top left to bottom right direction.
The determinant of a matrix is a value that can be calculated from the elements of the matrix. It gives information about the matrix such as whether it is invertible or singular.
To calculate the trace of a matrix, simply add up the elements on the main diagonal. For example, if a matrix is [1 23 4], the trace would be 1+4=5.
When the trace of a matrix is equal to the sum of its determinants, it means that the matrix satisfies the matrix trace theorem. This theorem states that the sum of the determinants of all submatrices of a matrix is equal to the trace of the matrix.
The trace of a matrix is important because it is a useful tool in linear algebra. It can provide information about the matrix, such as its eigenvalues, and can also be used to simplify calculations and proofs. Additionally, the trace of a matrix has applications in fields such as physics and engineering.