linear algebra – If \$ V_j = Ker (A- lambda I) ^ j \$, Why \$ dim (V_j) = r_i \$ if and only if \$ V_j = V_ {j + 1} \$?

If we have a matrix $$A$$ and the characteristic polynomial is $$(x- lambda_1) ^ {r_1} cdot … cdot (x- lambda_m) ​​^ {r_m}$$ and we define for each $$lambda_i$$, $$V_ {j} = ker (A- lambda I) ^ j$$. Why are there outings $$k$$ such as $$dimV_k = r_i$$and why does it hold if and only if $$V_k = V_ {k + 1}$$? Also, is it possible to have $$dimV_j> r_i$$? I've seen this on the algorithm to find the Jordan form, and I'm trying to understand why the algorithm works.