In some literature on linear algebra determinants play a critical role and are emphasized in the earlier chapters (see books by Anton & Rorres, and Lay). However in other literature it is totally ignored until the latter chapters (see Gilbert Strang). How much importance should we give the topic of determinants? I tend to use it to find linear independence of vectors and might extend this to finding the inverse but I think Gauss Jordan and LU might be easier for inverse. Does it have any other uses in Linear Algebra. Are there areas where determinants are used and have a real impact? Are there any real life applications of determinants? Is there a really good motivating example or explanation which will hook students into this topic? In linear algebra, where should determinants be placed? Like I said in my comment - in some literature it is at the beginning whilst in others it is bolted on at the end. I like the idea of checking if vectors are independent by using determinants so think they should be placed before independence of vectors. What do you think? If you teach a linear algebra course where do you place this topic.
What is the importance of determinants in linear algebra?
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linear-algebra
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education
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1Define "real" in "real impact"...Determinants appear in many places in algebra (not only linear but abstract), in analysis (Hessian, Jacobian, Wronskian, etc.), in differential equations, etc., etc., etc..... – 2012-06-20
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0As Peter pointed out, from the computational point of view, a determinant is expensive, so people try to avoid to compute it when dealing with large matrices. On the theoretical point of view, though, it plays an important role in many fields. – 2012-06-20
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0Before the eigenvalues-eigenvectors chapter. You need determinants to write the characteristic polynomial of a matrix... – 2018-07-29