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We (Prof. Wanmo Kang and Prof. Kyunghyun Cho) have been discussing over the past few years how we should teach linear algebra to students in this new era of data science and artificial intelligence. Over these discussions, which also led to some research collaboration as well, we realized that (one of the central concepts from linear algebra that is used frequently in practice, if not every day, was) the central concepts from linear algebra invoked frequently in practice, if not every day, were projection, and consequently singular value decomposition (SVD) as well as even less frequently positive definiteness. Unfortunately, we noticed that existing courses on linear algebra often focus much more on the invertibility (or lack thereof), to the point that many concepts are introduced not in the order of their practicality nor usefulness but in the order of the conveniences in mathematical derivations/introductions. We began to wonder a lot whether we can introduce concepts and results in linear algebra in a radically different way.

So, here’s a new textbook on linear algebra, where we re-imagined how and in which order linear algebra could be taught. Click the cover page below, or https://drive.google.com/file/d/1nJVwdQV9zp-Q9VQenZF0-HOOG6L2lEOD/view?usp=sharing, to download the full textbook. We also provide a version where we mix Korean and English, in order to help students who are more familiar with Korean follow the textbook more easily, at https://drive.google.com/file/d/1Qj8fnRZhgpcAHF2FTUhKTQQ0vZAFmrbv/view?usp=sharing.

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