441
edits
Linear Algebra (Book): Difference between revisions
m
no edit summary
No edit summary |
mNo edit summary |
||
| (7 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
{{InfoboxBook | {{InfoboxBook | ||
|title=Linear Algebra | |title=Linear Algebra | ||
| Line 13: | Line 12: | ||
|isbn13=978-0486635187 | |isbn13=978-0486635187 | ||
}} | }} | ||
The textbook '''''Linear Algebra''''' by [https://en.wikipedia.org/wiki/Georgiy_Shilov Georgi Shilov] | {{NavContainerFlex | ||
|content= | |||
{{NavButton|link=[[Read#Basic_Mathematics|Read]]}} | |||
}} | |||
The textbook [https://cosmathclub.files.wordpress.com/2014/10/georgi-shilov-linear-algebra4.pdf '''''Linear Algebra'''''] by [https://en.wikipedia.org/wiki/Georgiy_Shilov Georgi Shilov] thoroughly covers all major aspects of linear algebra, in addition it covers more geometrically motivated linear algebra in the latter half. | |||
This text can be viewed as an introduction to reading mathematics texts; The initial proofs are on arithmetic and properties of linear equations, and are more approachable than the manipulations of functions typical of analysis texts. It is difficult to overstate the universal importance of this subject, but it can be seen through reading. Linear algebra is the basis of all quantities of interest in physics, geometry, number theory, and the same techniques appear in engineering disciplines through physics, numerical computing, or machine learning. | |||
Another similarly famous Russian text on linear algebra would be [https://www.math.mcgill.ca/darmon/courses/19-20/algebra2/manin.pdf Kostrikin and Manin's Linear Algebra and Geometry] but better as a second casual read since it is more advanced. It contains more information about the interaction between linear algebra and quantum mechanics and relativity, and classcial projective geometry such as the Hopf fibration and Plücker coordinates. Projective geometries are treated concretely here, but are eventually characterized much more abstractly and generally in algebraic topology. | |||
== Table of Contents == | == Table of Contents == | ||
| Line 27: | Line 36: | ||
| 1.2 || Problems of the Theory of Systems of Linear Equations || 3 | | 1.2 || Problems of the Theory of Systems of Linear Equations || 3 | ||
|- | |- | ||
| 1.3 || Determinants of Order | | 1.3 || Determinants of Order <math>n</math> || 5 | ||
|- | |- | ||
| 1.4 || Properties of Determinants || 8 | | 1.4 || Properties of Determinants || 8 | ||
| Line 91: | Line 100: | ||
| 4.6 || The Range and Null Space of a Linear Operator || 93 | | 4.6 || The Range and Null Space of a Linear Operator || 93 | ||
|- | |- | ||
| 4.7 || Linear Operators Mapping a Space | | 4.7 || Linear Operators Mapping a Space <math>K_n</math> into Itself || 98 | ||
|- | |- | ||
| 4.8 || Invariant Subspaces || 106 | | 4.8 || Invariant Subspaces || 106 | ||
| Line 256: | Line 265: | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
{{Stub}} | |||