Bases and Dimension

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Related lectures (34)

Vector Spaces and Linear Applications Log in to Mediaspace to watch this video

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Linear Algebra in Dirac Notation Log in to Mediaspace to watch this video

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Linear Algebra: Change of Basis Log in to Mediaspace to watch this video

Covers the concept of changing bases in linear algebra, emphasizing the importance of understanding the process for various situations.

Orthogonal Bases in R^2 Log in to Mediaspace to watch this video

Explains orthogonal bases in R^2 and how to perform orthogonal projections.

Linear Algebra: Applications and Bases Log in to Mediaspace to watch this video

Explores unique solutions, linear dependence, canonical bases, and linear maps in linear algebra.

Linear Applications: Basis and Independence Log in to Mediaspace to watch this video

Covers linear independence, bases of vectors, and solving systems using matrices.

Steinitz Lemma and Cycles Log in to Mediaspace to watch this video

Explores the Steinitz Lemma and the concept of cycles in linear algebra.

Algebraic Varieties in Linear Algebra Log in to Mediaspace to watch this video

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

What is a (sub)manifold Log in to Mediaspace to watch this video

Introduces the concept of a submanifold in a linear space, defining it as a set smoothly embedded in the space.

Linear Transformations: Injective and Surjective Log in to Mediaspace to watch this video

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Single-Phase Sinusoidal Circuits Log in to Mediaspace to watch this video

Covers peak, mean, and rms values, average power, phase advance, and sinusoidal circuits.

Partial Differential Equations: Viscoelastic Materials Log in to Mediaspace to watch this video

Explores the application of PDEs in viscoelastic materials and materials science.

Gram-Schmidt Process Log in to Mediaspace to watch this video

Introduces the Gram-Schmidt orthogonalization process to find orthogonal bases for vector subspaces.

Multilinear Forms: Definitions and Properties Log in to Mediaspace to watch this video

Covers the definition and properties of multilinear forms, emphasizing linearity and applications in mathematics.

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