Lectures related to Canonical basis

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

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

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

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.

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

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

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

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

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 changing the base of linear applications and calculating vector images in different bases, emphasizing the use of canonical basis.

Explores linear transformations, matrices, injective and surjective functions, and their applications.

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

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