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Linear Algebra

Introduction

Main content

1. Vectors, Lines and Planes
2. Systems of Linear Equations, Vector Equations and Matrix Equations
3. Matrix Operations
4. Subspaces
5. Determinants
6. Eigenvalues and Eigenvectors
7. Orthogonality
8. Symmetric Matrices
9. Dynamical Systems

Appendices

10. Complex numbers
11. Proof of the existence of SVD
12. The inverse matrix theorem

Colophon

Acknowledgements

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Orthogonality

7. Orthogonality#

The concept of orthogonality is revisited. We see how we can find an optimally convenient basis to describe a subspace.

7.1. Orthogonal Complements
7.2. Orthogonal and Orthonormal bases
7.3. The Gram-Schmidt Process
7.4. Least Squares Solutions

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6.4. Complex Eigenvalues (and Eigenvectors)

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7.1. Orthogonal Complements

By a team of lecturers and developers from the Delft Institute of Applied Mathematics from the TU Delft University of Technology.

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