I have been wanting to learn about linear algebra (specifically about vector spaces) for a long time, but I am not sure what book to buy, any suggestions?
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I'm starting a very long quest to learn about math, so that I can program games. I'm mostly a corporate developer, and it's somewhat boring and non exciting. When I began my career, I chose it because I wanted to create games.  I'm told that Linear Algebra is the best place to start. Where should I go?
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Is it possible to get into algebraic geometry by just knowing calculus and linear algebra or is this too far of a stretch?  If not could anyone give me a list of book/lecture notes recommendations in chronological order to dive into algebraic geometry with my state of knowledge?  Thanks
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I'm interested in getting some books about multivariate analysis, and need your recommendations. Free books are always welcome, but if you know about some great non-free MVA book, please, state it.
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I am taking a course in Mathematical Methods for physicsPhysics (Junior Level).   We are working from   > Mathematical Methods for physicists, George B.Arfken .    I just need online resources covering ( Matrices, Determinants, Vector Analysis, Tensors and differential forms and Vector spaces...etc) to study and understand from.
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I'm a mathematics undergrad student who finished his first university year succesfully. For this post, it should be interesting to note that I already took a course in group theory.  I also had a course in linear algebra where we treated the following topics:  1) Vector spaces; basis; span; linear dependency; direct sum   2) Linear transformations, matrices, rank  3) Linear varieties, system of linear equations  4) Determinants  5) Eigenvalues and eigenvectors, diagonalisation, triangalisation, cayley-hamilton,  6) Euclidean spaces: inner products, norm, hermitian transformations, orthogonal basis, Gramm-Schmidt, orthogonal transformations  7) Prehilbert spaces  8) Isometries  9) Bilinear forms and quadrics in $2$ and $3$ dimensions  Now, I want to revise these topics, but it would be too boring to reread these books again, so now I look for a book that has all these topics, but also some additional requirements:   Focus on intuition (e.g. connections between linear algebra and geometry). This is a hard requirement for me, since there was no attention given to this in the course I took) Additional topics such as Jordan form of matrices, quotient vector spaces, ... Good exercises (preferred with solutions somewhere) The book must be rigorous   In the course I had, we mainly discussed finite-dimensional vector spaces, but I am also interested in a theory of infinite dimensional vector spaces.  Can someone hint me towards a good book that would suit me? If I have to add any information, please leave a comment and I will edit my post.  Thank you for your time.
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Ok, so I am reading about decision making and I came across this subject. Fortunately it has a  , but the point is I want to see some examples, and learn to solve regular problems of this field. Of course I can go for the book by Pontryagin but then I don't think that would be an educative book. Does anyone has a suggestion? I would be happy if it also covers LQ problems. P.S. I studied math, therefore I appreciate a book with rigorous approach to the subject.
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A week ago I  people on this site what mathematical background was needed for understanding Quantum Physics, and most of you mentioned Linear Algebra, so I decided to conduct a self-study of Linear Algebra. Of course, I'm just 1 week in, but I have some questions.    How is this going to be applicable to quantum physics? I have learned about matrices (addition, subtraction, multiplication and inversion) and about how to solve multiple equations with 3 unknowns using matrices, and now I am starting to learn about vectors. I am just 1 week in, so this is probably not even the tip of the iceberg, but I want to know how this is going to help me.  Also, say I master Linear Algebra in general in half a year (I'm in high school but I'm extremely fast with maths), what other 'types' of math would I need to self-study before being able to understand rudimentary quantum physics mathematically?
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Can someone give me a recommendation on homological algebra textbooks? I would like something that are accessible to a beginner (i.e., someone who have studied abstract algebra) and that have  1) an account on preadditive, additive, monoidal, abelian, triangulated categories, respectively,  2) motivations from algebraic topology exploited, (an elementary example that comes into my mind is the mapping cylinder/cone construction explained in contrast with Puppe sequence,)   3) an explanation on module theoretic topics like injective / projective resolutions,  4) a coverage of sheaf theory, cohomology of groups, and Galois cohomology.
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Do these three kinds of vector spaces, those with an inner-product, those with a norm and those with a metric, are the same sets of vector spaces? At least for finite dimensional vector spaces all of these coincide?   It would be great to know finite dimensional counter-examples if they exist any and if anyone can link to some lecture notes explaining this point.     Like are there examples of inner product spaces which cannot have a metric or metric spaces which cannot have a norm or various other such possible conflicts between these 3 properties.
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I've somehow managed to go through 3 years of my Maths degree without truly understanding what the term "finitely generated vector space" means.   Generated by what? Generating what? And for what? I have a very vague idea of what this term means and usually gloss over it when doing proofs but I think I just want a simple break-down of the meaning of this.
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During the next quarter at uni, I'll be taking a course in real analysis and since I prefer studying with an additional text I thought I'd come here to look for some book recommendations.  My background: I'm comfortable with linear algebra and single variable calculus, but shakey on multivariable calculus. I did have a slight introduction in to geometry.  For linear algebra I found the common recommendation of Hoffman &amp; Kunze to be very helpful (although the abstractness came as a bit of a kicker at first).   For Single variable calculus I used the book Calculus by Adams and Essex, which I found frustrating to work with, because it often left me guessing at what they were trying to do or why they were doing it. I also felt that they exercised a certain lack of rigour. (Which may be due to the subject which would make it hard to derive from axioms.)  Details: Though it would be a complementary text, I'd prefer one which will still hold value as a work of reference at a later point in my studies. I've heard that Rudin's Principles of mathematical analysis is one of the better textst out there, but also read several comments discouraging Rudin's book as a first introduction to real analysis, hence my quest to gather more information and maybe get some more personalised recommendations.  The course: The mandatory course literature will consist of lecture notes, but 4 texts are suggested as recommended reading.   T.M. Apostol, Mathematical analysis. Addison-Wesley (1974) J. Dieudonné, Foundations of Modern Analysis. Academic Press (1960) A. van Rooij, Analyse voor Beginners.Epsilon Uitgaven, no. 6 (2003)   R.S. Strichartz, The way of analysis (1995)   Thanks in advance!
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Been browsing around here for quite a while, and finally took the plunge and signed up.   I've started my mathematics major, and am taking a course in Linear Algebra. While I seem to be doing rather well in all the topics covered, such as vectors and matrix manipulation, I am having some trouble understanding the meaning of eigenvalues and eigenvectors.  For the life of me, I just cannot wrap my head around any textbook explanation (and I've tried three!), and Google so far just hasn't helped me at all. All I see are problem questions, but no real explanation (and even then most of those are hard to grasp).  Could someone be so kind and provide a layman explanation of these terms, and work me through an example? Nothing too hard, seeing as I'm a first year student.  Thank you, and I look forward to spending even more time on here!
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I want to start signal processing and I need a book that satisfies my mathematical requirements: I am in the third grade of high school and I don't know any useful thing about limit, differential, ...  Please help me.
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Since summer comes with a lot of spare time, I've decided to select a mathematical subject I want to learn as much as possible about over the next three months. That being said, number theory really caught my eye, but I have no prior training in it.   I've decided to conduct my studying effort in a library; I prefer real books to virtual ones, but as I'm not allowed to browse through the books on my own, I have to know beforehand what I'm looking for and this is where I'm kind of lost. I'm not really sure where to start.  Basically I wanna know about the following:    What are the prerequisites? (I'm currently trained in Linear Algebra, Calculus, Complex Analysis - all on an undergraduate level )  Can you recommend some reading materials?     Thank you.
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I'm looking for a book to learn Algebra. The programme is the following. The units marked with a $\star$ are the ones I'm most interested in (in the sense I know nothing about) and those with a $\circ$ are those which I'm mildly comfortable with. The ones that aren't marked shouldn't be of importance. Any important topic inside a unite will be boldfaced.  U1: Vector Algebra. Points in the $n$-dimensional space. Vectors. Scalar product. Norm. Lines and planes. Vectorial product.  $\circ$ U2: Vector Spaces. Definition. Subspaces. Linear independence. Linear combination. Generating systems. Basis. Dimesion. Sum and intersection of subspaces. Direct sum. Spaces with inner products.  $\circ$  U3: Matrices and determinants. Matrix Spaces. Sum and product of matrices. Linear ecuations. Gauss-Jordan elimination. Range. Roché Frobenius Theorem. Determinants. Properties. Determinant of a product. Determinants and inverses.  $\star$ U4: Linear transformations. Definition. Nucleus and image. Monomorphisms, epimorphisms and isomorphisms. Composition of linear transformations. Inverse linear tranforms.  U5: Complex numbers and polynomials. Complex numbers. Operations. Binomial and trigonometric form. De Möivre's Theorem.  Solving equations. Polynomials. Degree. Operations. Roots. Remainder theorem. Factorial decomposition. FTA. Lagrange interpolation.  $\star$ U6: Linear transformations and matrices. Matrix of a linear transformation. Matrix of the composition. Matrix of the inverse. Base changes.   $\star$ U7: Eigen values and eigen vectors Eigen values and eigen vectors. Characteristc polynomial. Aplications. Invariant subspaces. Diagonalization.   To let you know, I own a copy of Apostol's Calculus $\mathrm I $ which has some of those topics, precisely:   Linear Spaces Linear Transformations and Matrices.   I also have a copy of Apostol's second book of Calc $\mathrm II$which continues with   Determinants Eigenvalues and eigenvectors Eigenvalues of operators in Euclidean spaces.   I was reccommended Linear Algebra by Armando Rojo and have Linear Algebra by , which seems quite a good text.   What do you reccomend?
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I am very interested in studying modules, which I have studied algebra, is basic theory of groups and rings, of Hungerford and Dummit. I was reading the Dummit the module, but I still struggled a bit in the section and the tensor product of exact sequences, as in the book of Atiyah. They know a simple book to begin with?
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I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew