Remember that orthogonality means that U ⊤ U and V ⊤ V are equal to the identity matrix. This implies that we can also rewrite the decomposition as We can think of Y V and U ⊤ V as two transformations...

Remember that orthogonality means that U
^⊤U and V
^⊤V are equal to the identity matrix. This implies that we can also rewrite the decomposition as

We can think of Y V and U
^⊤V as two transformations of Y that preserve the total variability of Y since U and V are orthogonal.

Use the function svd to compute the SVD of y. This function will return U, V and the diagonal entries of D.

Compute the sum of squares of the columns of Y and store them in ss_y. Then compute the sum of squares of columns of the transformed Y V and store them in ss_yv. Confirm that sum(ss_y) is equal to sum(ss_yv).