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- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/05%3A_Linear_Transformations/5.06%3A_Isomorphisms/5.6E%3A_Exercises_for_Section_5.6This page contains exercises on linear transformations and isomorphisms in vector spaces, focusing on defining transformations from \(\mathbb{R}^3\) and \(\mathbb{R}^2\). It covers properties of isomo...This page contains exercises on linear transformations and isomorphisms in vector spaces, focusing on defining transformations from \(\mathbb{R}^3\) and \(\mathbb{R}^2\). It covers properties of isomorphisms, proving conditions for transformations, exploring matrix representations, and finding inverses. The content also discusses constructing matrices that uphold the structure of transformations and their inverses, particularly regarding spans of vectors in higher dimensions.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/zz%3A_Back_Matter/22%3A_7.5%3A_IndexThis page contains a comprehensive guide and glossary of key concepts in linear algebra, covering matrix operations, vector spaces, eigenvalues, and transformations. It includes definitions, theorems,...This page contains a comprehensive guide and glossary of key concepts in linear algebra, covering matrix operations, vector spaces, eigenvalues, and transformations. It includes definitions, theorems, properties, and examples on topics such as coordinates, bases, and dimensionality. Methods like Gaussian elimination and least-squares approaches are discussed.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/02%3A_Matrices/2.02%3A_The_Inverse_of_a_Matrix/2.2E%3A_Exercises_for_Section_2.2This page outlines exercises on matrix properties, particularly focusing on matrix inverses and related linear algebra concepts. It highlights critical examples, such as proving the identity matrix's ...This page outlines exercises on matrix properties, particularly focusing on matrix inverses and related linear algebra concepts. It highlights critical examples, such as proving the identity matrix's role, conditions for equality in matrix equations, and the existence of inverses. The exercises cover solving equations using matrix inverses, establishing unique inverses, and demonstrating properties of transposes and matrix products.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.02%3A_Eigenvalues_and_Eigenvectors_for_Special_Matrices/6.2E%3A_Exercises_for_Section_6.2This page contains exercises on computing eigenvalues and eigenvectors for various matrices, demonstrating similarities between matrices, and implications on their eigenvalues and eigenvectors. It inc...This page contains exercises on computing eigenvalues and eigenvectors for various matrices, demonstrating similarities between matrices, and implications on their eigenvalues and eigenvectors. It includes tasks involving elementary matrices for simplifying matrices and emphasizes properties of similar matrices concerning eigenvalues and eigenvectors.
