Thread: matrix question help

Consider a sequence of real numbers r1, r2 .... rn such that no two numbers are equal. Using these numbers, we create ( N x N) square matrix R such that the ( i, j)-th element of R is given by

ai, j = rk, where k = min(i, j), i = 1,2,...., N; j = 1,2,....,N.

Write the elements of matrix R in terms of real numbers r1,r2,....,rn. Clearly show at least the top 4 x 4 and all the elements on the four corners.

And is this a symmetric matrix?

need help anyone ?

This is how the matrix will look.


The argument goes like this for the first row and column the index of the elements will be and respectively so for all these elements we have . Now consider the sub-matrix by removing the first row and first column which is x but the index of the elements will be starting from 2 and repeat the argument.

Now you can answer the second question if the matrix is symmetric or not?
~Kalyan.

Am I right to say that

R^(T) = r1 r1 r1 r1
r1 r2 r2 r2
r1 r2 r3 r3
r1 r2 r3 r4

So they are SYMMETRIC.

Am I correct?

You are correct. The matrix is Symmetric.
~Kalyan.