Related lectures (47)
Harmonic Forms and Riemann Surfaces
Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.
Linear Maps and Bases: The Rank Theorem
Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.
Characteristic Polynomials and Similar Matrices
Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.
Diagonalization of Matrices and Least Squares
Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.
Linear Maps: Injectivity and Surjectivity
Explores injectivity and surjectivity in linear maps through examples and proofs.
Linear Applications: Matrices and Transformations
Covers linear applications, matrices, transformations, and the principle of superposition.
Linear Applications: Change of Basis
Explores changing the base of linear applications and calculating vector images in different bases, emphasizing the use of canonical basis.
Linear Combinations and Basis Characterization
Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.
Matrix Calculations: Basis Change and Extensions
Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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