A connected reference and learning path for linear algebra: linear systems, matrices, vector spaces, linear maps, orthogonality, eigenvalues, and applications.
Unless a node says otherwise, scalars lie in the same field, usually the real or complex numbers, and matrices and spaces are finite-dimensional. Individual results state additional hypotheses.
Complex inner products use $\langle x,y\rangle=x^*y$ (conjugate-linear in the first argument). Characteristic polynomials use the monic convention $p_A(t)=\det(tI-A)$. Definitions, theorems and algorithms are linked through the existing topic graph.
A connected reference and learning path for **linear algebra**: linear systems, matrices, vector spaces, linear maps, orthogonality, eigenvalues, and applications.
Start with [Linear algebra](https://knowen.md/nodes/23410), then study [linear systems](https://knowen.md/nodes/23411), [matrices](https://knowen.md/nodes/23447), [their connection](https://knowen.md/nodes/23751), [vector spaces](https://knowen.md/nodes/23775), and [applications](https://knowen.md/nodes/24113).
Unless a node says otherwise, scalars lie in the same field, usually the real or complex numbers, and matrices and spaces are finite-dimensional. Individual results state additional hypotheses.
## Start here
- [Study guide, conventions and references](https://knowen.md/nodes/37114)
- [Practice problems with worked solutions](https://knowen.md/nodes/37116)
- [Choosing factorizations and understanding numerical error](https://knowen.md/nodes/37115)
Complex inner products use $\langle x,y\rangle=x^*y$ (conjugate-linear in the first argument). Characteristic polynomials use the monic convention $p_A(t)=\det(tI-A)$. Definitions, theorems and algorithms are linked through the existing topic graph.
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