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I am given a matrix $N$ × $N$ symmetric positive definite matrix $B_N$

$$B_N = \begin{bmatrix} 2 & -1 & 0 & 0 & \cdots & \cdots\\ -1 & 2 & -1 & 0 & \cdots & \cdots\\ \vdots & \vdots & \ddots & \cdots & \cdots & \cdots \\ \vdots & \vdots & \vdots & \ddots & \cdots & \cdots \\ \vdots & \vdots & \vdots & \vdots & \ddots & -1 \\ \vdots & \vdots & \vdots & \vdots & -1 & 2 \\ \end{bmatrix}$$

$C_N$ is a $N \times (N+1)$ matrix with entries equal to $1$ on the main diagonal and equal to $−1$ on the upper diagonal, and with all the other entries equal to $0$ i.e.

$$C_N = \begin{bmatrix} 1 & -1 & 0 & 0 & \cdots & \cdots & \cdots\\ 0 & 1 & -1 & 0 & \cdots & \cdots & \cdots\\ 0 & 0 & 1 & -1 & \cdots & \cdots & \cdots\\ \vdots & \vdots & \vdots & \ddots & \cdots & \cdots & \cdots\\ \vdots & \vdots & \vdots & \vdots & \ddots & -1 & \cdots\\ \vdots & \vdots & \vdots & \vdots & \vdots & 1 & -1 \end{bmatrix}$$

I have to show that $B_N = C_N C_N^T$.

I am badly stuck. Any idea how to approach this question.

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    I rewrote the entire question. Kindly use $\LaTeX$ in the future. What have you tried so far? All you need to do is just matrix matrix multiplication.2012-03-14
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    Thanks Sivaram. So far I am able to show that A(i,i) is 2 , I am doing that by working on a 3X3 matrix and 4 X 4 matrix.
    u =
    1 -1 0
    0 1 -1

    octave-3.2.4.exe:54> transpose(u)*u
    ans = 1 -1 0
    -1 2 -1
    0 -1 1
    2012-03-14

3 Answers 3