Lecture 1

Question 1

Make Python wait

Answer 1

from time import sleep

sleep(0.1)

Question 2

t(n) = O(g(n)) definition

Answer 2

There is C s.t. t(n) <= C.g(n)

Question 3

Matrix product numpy

Answer 3

import numpy as np

np.dot(A,B)

Question 4

Prove linear independance

Answer 4

Show that det([v1 v2 v3]) is not null (with np.linalg.det())

Question 5

Nullspace of a matrix

Answer 5

Dimension of nullspace = dimension - rank

Rank is the number of vectors so that the matrix is linearly independent.

Question 6

Inverse of a matrix

Answer 6

np.linalg.inv()

Question 7

Operations of symmetric matrices

Answer 7

AB+BA is symmetric
A-B, A+B, A-1, A^n, cA too
(symmetric if A^T = A)