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Linear Algebra

Linear algebra is the study of vector spaces, that we have already introduced as a special kind of algebraical structure, and linear maps between those vector spaces. We will introduce the theory step by step, starting with systems of linear equations emphasizing Euclidean spaces and matrices, and moving on to abstract spaces and linear maps.

| | | | created: 2014-02-20 22:21:30 | modified: 2020-11-29 05:50:03 | by: bookofproofs | references: [561], [979], [1038]

1.Introduction to Matrices and Vectors

2.Linear Equations and Systems of Linear Equations (SLEs)

3.Vectors Revised - Vector Spaces

4.Vectors

5.Eigenvalues and Eigenvectors

6.Principal Axis Transformation

7.Jordan Normal Form

8.Rotations and Basic Transformations

9.Determinants

10.Affine Spaces

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[561] Koecher Max: “Lineare Algebra und analytische Geometrie”, Springer-Verlag Berlin Heidelberg New York, 1992, 3 Volume

[979] Reinhardt F., Soeder H.: “dtv-Atlas zur Mathematik”, Deutsche Taschenbuch Verlag, 1994, 10

[1038] Wille, D; Holz., M : “Repetitorium der Linearen Algebra”, Binomi Verlag, 1994