Recipes: the determinant of a 3 × 3 matrix, compute the determinant using cofactor expansions. Vocabulary words: minor, cofactor. In this section, we give a recursive formula for the determinant of a matrix, called a cofactor expansion. The formula is recursive in that we will compute the determinant of an n × n matrix assuming we already Calculations of determinants is a common and also a compulsory task in the Linear Algebra courses taught in engineering schools. Although there are several methods to approach it in a simple way, like is the case of the cofactors method, it must be taken into account that as the size of the determinant increases, for example for 4 × 4 and 5 × 5 matrices, the calculations become more and more Step 4: Multiply by 1/Determinant. Now find the determinant of the original matrix. This isn't too hard, because we already calculated the determinants of the smaller parts when we did "Matrix of Minors". Using: Elements of top row: 3, 0, 2 Minors for top row: 2, 2, 2. We end up with this calculation: Determinant = 3×2 − 0×2 + 2×2 = 10 The determinant function now returns a vector float, each element is nearly equal (nearly due to the floating point precision) to the determinant of the matrix. The algorithm is the same as before. A multiplication is computed between a row or a column with the corresponding value in the cofactor matrix, all values are added together. The DFT is (or can be, through appropriate selection of scaling) a unitary transform, i.e., one that preserves energy. The appropriate choice of scaling to achieve unitarity is , so that the energy in the physical domain will be the same as the energy in the Fourier domain, i.e., to satisfy Parseval's theorem. (Other, non-unitary, scalings, are aQ08P7.

determinant of a 4x4 matrix example