Textbook Guide Mathematics: Coordinate Vector, Centroid, Positive Definiteness
Document Summary
Chapter 7: symmetric matrices and quadratic forms. A symmetric matrix say a is said to be a symmetric matrix if and only if a = a. T and for this property to be true, the matrix a should always be a square matrix in order to be a symmetric matrix. While the values on the diagonal can remain any random values, the other values always occur in pairs at opposite positions aligned as per the main diagonal. For a matrix a which is symmetrical, any two given eigenvectors from two different eigenspaces will be orthogonal to each other. For the completion of such a diagonalization we must first calculate the n eigenvectors which are linearly independent and orthonormal. In case a is orthogonally diagonalizable as in the above equation then the below equation holds true also stating the fact that a is symmetric, At = (pdpt) t = ptt dt pt = pdpt = a.
