Question

G=(1)/(25)([52,0,36],[0,100,0],[36,0,73]) (a) What is the minimal number N of data points that could have resulted in this Gram matrix?

Answer 1

The minimal number of data points that could have resulted in this Gram matrix is 121.

Step-by-step explanation:

The Gram matrix, G, represents the inner products of vectors in a given set. In this case, G=(1/25)([52,0,36],[0,100,0],[36,0,73]). To determine the minimal number, N, of data points that could have resulted in this Gram matrix, we need to find the square root of the determinant of G.

First, calculate the determinant of G: det(G) = (1/25)(52 * 100 * 73) = 14656.

Next, take the square root of the determinant: N = sqrt(14656) = 121.

Therefore, the minimal number of data points that could have resulted in this Gram matrix is 121.