LDL^T decomposition of a symmetric tridiagonal matrix

[ChEJosh]

I have to do a LDL$$^{T}$$ transform of a symmetrical matrix:

[2 -1 0]
[-1 2 -1]
[0 -1 2]

And, I'm just wondering if I have to do a row exchange, or something. I can't remember if the L matrix has to have the form

[x 0 0]
[x x 0]
[x x x]

where the x's are nonzero numbers.

Basically, I'm asking if that 0 in the lower left hand corner is all right, and if I only need to eliminate the -1 at positions 2,3 and 1,2

Thank you.

 

[HallsofIvy]

Yes, L is, by definition, a "Lower Triangular" matrix. It must have only 0s above ther diagonal. It is not required that all other numbers not be 0.