On page 183 of this book there is **Theorem 3**:

In other words, if the spectral radius of a matrix `B`

is less than 1, there must be a norm $ ||B||_{p}$, so that $||B||_{p}<1$.

```
N(Eigenvalues(MatrixForm({{0, -1, 0}, {0, 1/2, 1}, {0, 1/5, 2/5}})))
```

But the following norms are all greater than 1:

```
N(Norm(MatrixForm({{0, -1, 0}, {0, 1/2, 1}, {0, 1/5, 2/5}}), 1))
N(Norm(MatrixForm({{0, -1, 0}, {0, 1/2, 1}, {0, 1/5, 2/5}}), 2))
N(Norm(MatrixForm({{0, -1, 0}, {0, 1/2, 1}, {0, 1/5, 2/5}}), Infinity))
```

What can I do to find the p-norm that makes $||A||_{p}<1$ hold?

**Related exercises(2001武汉 岩石 数值分析):**