Matrix Analysis
by Roger A. Horn, Charles R. Johnson · first published 1990
64% recommend36% neutral
Why HN recommends it
A thorough, rigorous reference on advanced matrix theory, with end-of-chapter problem sets. Suited to readers seeking deeper linear algebra or a reference for applied math and statistics.
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Advanced Linear Algebra, Roman; Linear Algebra, Hoffman & Kunze; Matrix Analysis, Horn & Johnson; Principles of Mathematical Analysis, Rudin; Real Analysis, Royden. Miscellaneous comments: - Reading pure abstract algebra (e.g. Dummit & Foote) isn't a good use of time if you intend…
on “Ask HN: Learning advanced math” ↗…this... Also there are really good books out there and linalg is a must nowdays. As for textbook: http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mat... As for reference: http://www.amazon.com/Matrix-Analysis-Roger-Horn/dp/05213863...
on “Linear algebra tutorial in four pages” ↗Thanks for pointing out TLA! Hawking was great, and wrote a fantastic book called "God Invented the Integers" where he details fascinating seminal math contributions. I'm a geek for Horn and Johnson of Matrix Analysis fame. Munkres topology has been bedtime reading for a long time. Quite a few philosophers strike my fancy, especially the existential school.
on “Dijkstra: Philips and I – a few snapshots (2001) [pdf]” ↗I'm coming from an applied math perspective. A few of my favorites (and ones I find myself regularly referring to) are: Matrix Analysis by Horn and Johnson (perhaps the best end-of-chapter problem sets of any math book I've encountered!) Matrix Computations by Golub and Van Loan Elements of Statistical Learning by Hastie, Friedman,…
on “Ask HN: Math books that made you significantly better at math?” ↗Matrix Analysis by Horn and Johnson is another great book, though it is a bit pricier than a Dover book.
on “Mathematicians prove Pólya's conjecture for the eigenvalues of a disk” ↗if you're relearning, you should use Horn and Johnson's Matrix Analysis IMO
on “Proposal: Linear Algebra Study Group” ↗If you want a more advanced book I really strongly recommend Matrix Analysis and it's Applications by Carl Meyer. Very clear and concise and the problems are well written. It's my all time favorite math book. But this is really if you want to absorb a lot of more-advanced linear…
on “Linear Algebra Done Right Video Series” ↗…That was me. I was great at calculus type things, but Matrix Theory hit me like a ton of bricks. I still have that text book, sitting on my other desk, staring menacingly at me from across the room; Matrix Analysis, Horn and Johnson. Geometry in High School gave me a taste, but would have been nice had we had available another proof based class in the math curriculum; Formal Logic or Discrete Maths at a high school…
on “The Calculus Trap (2005)” ↗> That was me. I was great at calculus type things, but Matrix Theory hit me like a ton of bricks. I still have that text book, sitting on my other desk, staring menacingly at me from across the room; Matrix Analysis, Horn and Johnson. Geometry in High School gave me a taste, but would have been nice had we had available another proof based class in the math curriculum; Formal Logic or Discrete Maths at a high school…
on “The Calculus Trap (2005)” ↗It's a master degree course called Matrix Analysis (e.g Horn and Johnson as text).
on “Seven sins of numerical linear algebra” ↗You ever hear of Horn from Horn & Johnson fame (Matrix Analysis)? Guy had a 9-5 for years and researched at nights in his home office. That would be my ideal setup, I think.
on “The Ph.D Bust: America's Awful Market for Young Scientists” ↗Sheldon Axler book for some reason is hugely hyped in HN always when this topic comes up. But I do wish for a more comprehensive book on Algebra covering the entire breath of the field. Matrix Analysis by Roger A Horn, seems a good book with most of the knowledge of matrices covered. Could be helpful for people working with Graphics.
on “Ask HN: What are you learning?” ↗…for a citation as the words definitely are real but the claim sounded hyperspecific and unfamiliar. I figure a person needs 12 to 18 months of linear algebra, enough to work through Horn and Johnson's "Matrix Analysis" or the more bespoke volumes from Jeffrey Humpheries to get the math behind ML. Not necessarily to use AI/ML as a tech, which really can benefit from the grind towards commodification, but to be able…
on “LLM from scratch, part 28 – training a base model from scratch on an RTX 3090” ↗…here is the polar decomposition. (3) Get some contact with some applications, including in elementary multi-variate statistics, numerical techniques, optimization, etc. (4) Pick from Horn and Johnson, Matrix Analysis. and Horn and Johnson, Topics in Matrix Analysis. My first course was an "advanced course" from one of Horn, Johnson, and I knocked the socks off all the other students. How'd I do that? Brilliant?…
on “Ask HN: Learning advanced math” ↗