Compute t(A). t(A) means the transpose of matrix A; it is performed by switching the rows and columns for each index.
Compute t(A)A by matrix multiplication.
Calculate the eigenvalues of t(A)A. If you do not know how to do this, refer to the Resources section for a guide.
Take the square root of the eigenvalues and put them in descending order. These values are called the singular values of A.
Create the diagonal matrix S with the singular values in descending order being its elements.
Compute S-1. S-1 is the inverse of S. If you do not know how to calculate it, refer to the Resources section for a guide.
Calculate the eigenvectors for t(A)A.
Create a new matrix, V, using the eigenvectors you just computed. The eigenvectors should be the columns of V.
Compute t(V).
Calculate U = AVS-1 by matrix multiplication.
Get the final singular value decomposition by writing A as A = USt(V).