https://www.chenk.top/en/tags/tensor-decomposition/Recent content in Tensor Decomposition on Chen Kai BlogHugoenWed, 26 Mar 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/13-tensors-and-multilinear-algebra/Wed, 26 Mar 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/13-tensors-and-multilinear-algebra/<p>If you&rsquo;ve used PyTorch or TensorFlow, you&rsquo;ve met the word &ldquo;tensor&rdquo; hundreds of times. PyTorch calls every array <code>torch.Tensor</code>; TensorFlow puts it in the product name. But what <em>is</em> a tensor, and why did frameworks borrow this physics-flavored word for what looks like a multi-dimensional array?</p> <p>The short answer from this chapter:</p> <blockquote> <p>A tensor is the natural generalization of a scalar, vector, and matrix to <strong>arbitrary</strong> dimensions. Everything you know about matrices either lifts cleanly to tensors, or breaks in instructive ways.</p>