https://www.chenk.top/en/tags/tensor-networks/Recent content in Tensor Networks on Chen Kai BlogHugoenWed, 30 Apr 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/18-frontiers-and-summary/Wed, 30 Apr 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/18-frontiers-and-summary/<p>We have walked the long road of linear algebra together. We started with arrows in the plane and ended at the gates of quantum computers, the inner workings of large language models, and the topology of data clouds. The remarkable thing — the thing this series has tried to make visible — is that the same handful of ideas keeps coming back. A vector is a state. A matrix is a transformation. A decomposition is the structure hiding inside the transformation. A norm tells you when you can trust your computation. Once you internalise that loop, every &ldquo;frontier&rdquo; looks less like a foreign country and more like another dialect of a language you already speak.</p>