Linear Algebra and Matrices Flashcards
How is the nullspace of a matrix defined?
The set of all vectors x, that satisfies the equation Ax = ZeroVektor
What is Nullity of Matrix
and which is it’s relation the the Rank?
The Nullity is the number of vectors in the null spact. Relation: NumberOfColumns = Rank + Nullity
What can I say about the rank of a matriz of Order x (x,x), if the det != 0 ?
The rank is x
what are the errors in the following function to evaluate wheter if a,b,c are right angled or not:
#ENTER YOUR CODE BELOW
def triangle_right_angled(a, b, c):
import math
return (c ** 2 == a ** 2 + b ** 2)
comparison between float numbers => give forecarst of small number, no exact comparison
c ** 2 - a ** 2 - b ** 2 <= 10 ** -6
should allow for arbitrary (unsorted) lengths => first define catetes and hip
how to increment the dic resources on key ingredient by the value of amount?
resources[ingredient] += amount
explain the row and column pictures for the linear equation A x = b in R2
- row picture: get two points for each row in equation (e.g. replace one of the var. by zero) to plot lines. The solution will be the intersection
- column picture: plot the column vectors and the point b. the x vector defines how much do I need from each column vector to reach b.
in which vector space will be A . x always?
C(A) : column space of A
which kind of functions can be represented as matrix?
linear functions
what is the geometrical interpretation of the determinant? How can I trlate it to condition fol solving Ax = b?
det(A) is the vol of the unity cube x after Ax. If A.x applied to the unity cube x, can I find A-1 ? If A squishes the unity cube I can’t. In this case det(A) = 0 and I can’t solve Ax = b.
if one eingenvalue of a square matrix is zero then ….
The det o the matrix is zero
what does the function call np.linalg.eig(Q) returns?
a tuple with eigenvalues and eigenvectors of Q
