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Concept

Canonical basis

Related lectures (29)

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

Explores canonical basis, linear mapping, and eigenvalues in linear algebra.

Introduces linear applications in 3 dimensions, defining them as functions that preserve vector addition and scalar multiplication.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Explores the importance of modal analysis in understanding mechanical modes and their resonance frequencies.

Covers vector spaces, bases, and decomposition of vectors in R³.

Covers matrix representations of linear applications in R³ and the invariance of rank.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Explores diagonalization through projectors and matrices of projection in relation to eigenvalues and eigenvectors.

Covers vector spaces in R2 and R3, including examples of proportional families and coordinate transformations.

Explores the diagonalization of linear maps by finding a basis formed by eigenvectors.

Explores controllability in state-space models, state transformations, and their impact on state gain.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Explores bases and vector subspaces in R³, discussing properties and examples of bases.

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

Covers the proof of primary decomposition theorem for endomorphisms of finite-dimensional vector spaces.

Covers preliminary concepts in signals and systems, including linear systems invariant in time and stability.

Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.

Explores injectivity and surjectivity in linear maps through examples and proofs.

Covers linear applications, matrices, transformations, and the principle of superposition.