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(A) Show that the Frobenius norm is also the square root of the sum of the squared singular values.

In this problem, you’ll look at singular value decomposition as a way to find a low-rank approximation to a matrix.

(A) Upload any (tasteful) image you want to Colab. Note that life is a little easier if you put it in your Google drive and access it from there so you don’t have to constantly re-upload it every time you come back after a break. Load the image as a NumPy array. There are various ways to do this, but the easiest may be to use from matplotlib. There is a useful tutorial also. Once you have a NumPy array, look at its ss probably 푤푖푑푡ℎ × ℎ푒푖푔ℎ푡 × 3 or somethi that effect, with the third dimension usually reflecting red, green, and blue channels. Make the image grayscale by taking the mean across this third dimension. This should make it into a 푤푖푑푡ℎ × ℎ푒푖푔ℎ푡 array. Use imshow as in previous homeworks to render the grayscale image.