Linear algebra

Linear algebra is a branch of mathematics that concerns linear equations, vector spaces, linear maps between vector spaces, and matrices.

Featured Projects
We have two featured projects, both outside the namespace of this resource.


 * Mathematics for Applied Sciences (Osnabrück 2023-2024)/Part I is a mathematical course for beginners at the University of Osnabrück. It covers logical foundation, sets, mappings, algebraic structures like fields and polynomials, the basics of analysis like sequences, continuity, differentiability, primitive functions and the basics of linear algebra like vector spaces, bases, linear maps, eigenvalues. While course has been taught many times, this is a textbook -- not an online course.


 * Contents • Linear systems• Matrices and vector spaces• Bases and dimension• Linear mappings• Invertible matrices• Determinants• Eigenspaces• Diagonalizability

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 * Tensors employs the "unorthodox" approach of using the covariant and contravariant forms associated with Ricci calculus. But keep in mind that this approach is vastly superior. It is required for General Relativity, and is the most powerful way to do vectors and tensors.


 * Contents: • Tensors/Definitions • Tensors/Bases • Tensors/Calculations with index notation • Tensors/Transformation rule under a change of basis

Other projects

 * /Introductory definitions/ is a short and simple introduction to linear algebra. The best part is the three links to three Youtube videos:
 * Element-wise Matrix Operations
 * Matrix multiplication
 * Gaussian Elimination


 * /Linear equations/ is a beginners guide to equations like the famous y=mx+b. In the US, this material is typically introduced in late middle school or early high school.
 * /Determinant quiz/ is a 3-question quiz on finding the determinants of square matrices. We need more quizzes on linear algebra. Teachers are encouraged to task students with writing and publishing quizzes on Wikiversity (see the Call for contributions below.)
 * Orthogonal matrix attempts to visualize orthogonality and rotational transformations in non-rigorous fashion.
 * /Linear maps/ Defines the linearity relevant to this algebra in recondite mathematical language.
 * /Convex combination/. In convex geometry, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.tion/]].
 * /Cramer's rule/ attempts to simplify what can be found in Wikipedia's Cramer's rule, while the attempt is successful, the Wikipedia article is fairly readable. In the US, the rule is typically taught soon after a student completes a year of college-level calculus.

Call for contributions
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