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Related lectures (13)

Explores the properties and operations of complex numbers in mathematics.

Covers the explicit computations of nerves of categories and geometric realisations of simplicial sets.

Explores the Spectral Theorem, emphasizing the Min-Max Criterion for symmetric matrices and the properties of positive definite matrices.

Explores Sylvester's Theorem and the importance of orthogonal bases in linear algebra.

Explores constructing matrix transformations in IR4 using canonical bases and the importance of the equality [T]BB' = [id].

Explores orthogonality, eigenvalues, and diagonalization in linear algebra, focusing on finding orthogonal bases and diagonalizing matrices.

Covers the exercise on determining key parameters of a common source amplifier.

Covers the isoparametric formulation in the context of the finite element method.

Explores the properties of the Gumbel distribution and its application in the coupon collector problem with illustrative examples.

Explores norms, orthogonality, and the Pythagorean theorem in vector spaces.

Covers Cramer's Rule for solving linear equations using determinants.

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

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