Become a Linear Algebra Master
What you will learn
Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination
Operations on two matrices, including matrix multiplication and elimination matrices
Matrices as vectors, including linear combinations and span, linear independence, and subspaces
Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities
Matrix-vector products, including the null and column spaces, and solving Ax=b
Transformations, including linear transformations, projections, and composition of transformations
Inverses, including invertible and singular matrices, and solving systems with inverse matrices
Determinants, including upper and lower triangular matrices, and Cramer's rule
Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose
Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis
Orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process
Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions
Course Gallery
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Comidoc Review
Our Verdict
As a seasoned e-learning critic, I find Become a Linear Algebra Master not only covers all essential linear algebra topics, but also does so in an engaging and accessible way. Students praise instructor Krista King's teaching style for her expertise in breaking down complex ideas so they are easily understood. The course format of "read, watch, and solve" ensures that learners can reinforce their understanding through practical exercises. Moreover, the high-quality video content is supplemented by plentiful examples and quizzes that allow students to practice learned concepts. However, there are opportunities for improvement. Integrating proofs into the curriculum could strengthen the course, even if they were sourced externally. Similarly, additional context on practical applications could help illustrate the relevance of these mathematical principles in real-world situations. Some users mention navigation issues and isolated instances where external research might be necessary to clarify concepts fully. Despite this, Become a Linear Algebra Master excels at teaching complex ideas with clarity, making it an effective learning platform for aspiring linear algebra masters.
What We Liked
- The course covers all critical topics of linear algebra in an accessible and thorough manner
- Krista King is praised for her ability to explain complex concepts in easy-to-understand bits
- 'Read, watch, and solve' pattern helps reinforce learning effectively
- High quality video content with plenty of examples and quizzes to practice
Potential Drawbacks
- Lack of proofs within the course could be improved by linking external resources
- A few reviewers mention that real-world applications are not fully addressed
- Initial uncertainty in navigation is noted, but expected to improve with later updates
- Infrequent instances where additional clarification might require external research