Now that you have had some practice working with vectors and matrices, create a notebook using your new skills that addresses the problems below: 1. Create the vector, c = [5,2,8), and calculate its L2-norm and L1-norm (replace p= 2 with p = 1 in the p-norm equation above). 2. Create another vector, y= (1,3,2), and calculate both the Euclidean and Cosine distances between y and the vector 2. 3. Create and pretty-print the following matrix. 1 2 3 6 A= 7 8 9 10 11 12 13 14 15 4. Multiply A by 2 and y, respectively. That is, calculate Ax and then Ay. Be sure to pretty-print each result. 5. Create the following matrix, B, and then compute the result of AB. 1 2 3 B= 5 6 7 8 9 10 11 12 6. Calculate the pairwise Euclidean distance matrix for the row-vectors in A (pretty-print the result(s)). 7. Calculate the square 3x3 matrix C = BBT (pretty-print the result(s)). 8. Calculate the Eigen Decomposition for C (pretty-print the result(s)). 9. Use the Q and A matrices from Problem 8 to numerically recalculate C (don't forget to pretty-print the result). 10. Calculate the Singular Value Decomposition for C (pretty-print the result(s)). 11. Use the U, 2, and VT matrices from Problem 10 to numerically recalculate C (don't forget to pretty-print the result). Now that you have had some practice working with vectors and matrices, create a notebook using your new skills that addresses the problems below: 1. Create the vector, c = [5,2,8), and calculate its L2-norm and L1-norm (replace p= 2 with p = 1 in the p-norm equation above). 2. Create another vector, y= (1,3,2), and calculate both the Euclidean and Cosine distances between y and the vector 2. 3. Create and pretty-print the following matrix. 1 2 3 6 A= 7 8 9 10 11 12 13 14 15 4. Multiply A by 2 and y, respectively. That is, calculate Ax and then Ay. Be sure to pretty-print each result. 5. Create the following matrix, B, and then compute the result of AB. 1 2 3 B= 5 6 7 8 9 10 11 12 6. Calculate the pairwise Euclidean distance matrix for the row-vectors in A (pretty-print the result(s)). 7. Calculate the square 3x3 matrix C = BBT (pretty-print the result(s)). 8. Calculate the Eigen Decomposition for C (pretty-print the result(s)). 9. Use the Q and A matrices from Problem 8 to numerically recalculate C (don't forget to pretty-print the result). 10. Calculate the Singular Value Decomposition for C (pretty-print the result(s)). 11. Use the U, 2, and VT matrices from Problem 10 to numerically recalculate C (don't forget to pretty-print the result)
