## Background :

I use Julia to construct Symmetric normalized Laplacian matrix L^{sym} (Matrix D is a diagonal matrix):L^{sym}=D^{-1/2}×L×D^{-1/2}. Matrix L^{sym} is a sparse matrix.

My computer configuration:

```
julia> versioninfo()
Julia Version 1.2.0
Commit c6da87ff4b (2019-08-20 00:03 UTC)
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: Intel(R) Core(TM) i5-3337U CPU @ 1.80GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-6.0.1 (ORCJIT, ivybridge)
```

## My code:

```
D = ... # sparse matrix
L = ... # sparse matrix
Lsym = D^(-0.5)*L*D^(-0.5)
```

## Question:

- When L is 10000 × 10000 sparse matrix , the calculation speed of L^{sym} is fine.
- When L is 100000 × 100000 sparse matrix , the calculation speed of L^{sym} is very slow.

I wonder if there’s a faster way to calculate L^{sym}, or my code has problems calculating large sparse matrix.