Attribute | Rank |
---|---|

Difficulty | 2-5 (depending on chapter) |

Proof Quality | 3 |

Readability | 3 |

Self-Study | 2 |

Good for Teaching? | 3 |

Quality of Exercises | 3 |

- vector spaces introduction
- direct sums

- spanning sets, linear independence, basis, and dimensions
- linear maps
- null spaces, ranges
- matrix of a linear map
- invertibility

- eigenvalues and eigenvectors
- introduced via invariant subspaces
- polynomials on operators
- upper triangular matrices and invariant subspaces

- inner product spaces, norms, and orthonormal bases
- orthogonal projections
- linear functionals and adjoints

- self-anoint and normal operators
- the spectral theorem
- isometries
- singular-value decompositions
- generalized eigenvectors, nilpotent operators, and the characteristic polynomial
- minimal polynomial
- Jordan basis
- trace and determinant of a matrix