geometric multiplicity and algebraic multiplicity are equal for symmetric matrice

𝜆$\lambda$ be an eigen value of a symmetric matrix 𝐴$A$ then how to show that the geometric multiplicity and algebraic multiplicity are equal?

in general, geometric multiplicity <= algebraic multipliciy

https://youtu.be/Xcln3xG8QGQ

weighted adjacency matrix

Q: 0 means no link. but small value means a very close link.

In igraph, direction is from Column to row. The following example show arrow from 2nd and 3rd to 1st.

In Yuan, network exact control paper, the directions are from row to columns. So, is the transpose of the igraph adjacency matrix.