Recent content by Diffie Heltrix

Again, given vector ##x\in\mathbb{R}^n##, How can I define the norm associated with ##A## (denoted by ##|||\cdot|||_A##) s.t. ##|||Ax|||_A \ge c |||x|||_A## (where ##c>1##)? What is the connection to the minimal eigenvalue exactly?

So how the norm is defined precisely? Maybe $|||x|||_A=\lambda_i ||x||_1$? How lambda_i is connected here?

So You map every $x=Id\cdot x$ to 1? That's not a norm.

Suppose we pick a matrix M\in M_n(ℝ) s.t. all its eigenvalues are strictly bigger than 1. In the question here the user said it induces some norm (|||⋅|||) which "expands" vector in sense that exists constant c∈ℝ s.t. ∀x∈ℝ^n |||Ax||| ≥ |||x||| . I still cannot understand why it's correct. How...