Bilinear Forms: Theory and Applications

Related lectures (27)

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Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Discusses quadratic forms, matrix diagonalization, and their applications in optimization problems.

Explores the definition and properties of Hermitian forms in complex vector spaces.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.