I am curious as to how geometric intuition gradually developed in linear algebra. Are there articles that narrate how visualization became popular in this field? I think its important to know this as it might help us recognize the opportunity to do the same for other fields of mathematics when it arises.
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3Analytic geometry has shaped linear algebra a lot, see books with the title "Analytic geometry and Linear Algebra". – Dietrich Burde Feb 27 '18 at 14:46
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3Geometry is much older than linear algebra. The geometric ideas came first, and the linear algebra was developed with them in mind. – Robert Israel Feb 27 '18 at 14:52
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@Dietrich Burde: does it tell how visualization crept into the field. From wikipedia, linear algebra started with determinants. I can only imagine, probably, during the late 1800s up to the mid 1900s that linear algebra is mostly thought of in a very algebraic and formal manner with no reference to intuition. I am curious as to how geometric intuition developed from something that has little no relation to geometry...? – TheLast Cipher Feb 27 '18 at 14:52
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"no relation to geometry"? Determinants have a close relation, see volume. – Dietrich Burde Feb 27 '18 at 14:53
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@RobertIsrael: So linear algebra sprouted from analytic geometry? – TheLast Cipher Feb 27 '18 at 14:54
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@DietrichBurde: Determinants have a close relation to geometry, I understand that. But what I meant that possibly, during its early stages of development that it possibly was not seen as closely related. I am curious as to how people connected determinant to the idea of area and volume in geometry. – TheLast Cipher Feb 27 '18 at 14:56
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1It was, as Robert says, the other way around. The volume of a parallelepiped motivated the determinant, see this MSE-question. – Dietrich Burde Feb 27 '18 at 14:57
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Cool! Thank you for the link. – TheLast Cipher Feb 27 '18 at 14:59
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2You might look at the Mactutor page Matrices and Determinants – Robert Israel Feb 27 '18 at 15:10