Lectures related to Operations on Linear Applications

Linear Transformations in R³

Covers operations on linear applications in R³, including composition, addition, and determinants.

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Matrix Operations: Definitions and Properties

Covers the definitions and properties of matrices, including matrix operations and determinants.

Characteristic Polynomials and Similar Matrices

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

Geometric Transformations in R2 and R3

Explores geometric transformations in R2 and R3, including linear transformations, projections, matrices, and trace properties.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Matrix Representations: Linear Maps

Explores matrix representations of linear maps and their invariance, using examples and special cases.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Linear Algebra: Rank Theorem

Explores the Rank Theorem in linear algebra, covering matrix properties and determinants.

Linear Algebra: Compositions of Applications

Explores compositions of applications and injectivity conditions in linear algebra, including restriction of applications and combinatorial proof of injections.

Linear Transformations: Injective and Surjective

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

Linear Algebra: Multilinear Groin and Determinants

Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.

Linear Applications: Matrices and Transformations

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

Determinants of Matrices: Properties and Applications

Explores the properties and applications of determinants of matrices in linear algebra.

Linear Algebra: Matrices and Inverses

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Linear Algebra in 3D: Determinants and Inverses

Explores determinants in 3D space and their role in linear algebra.

Matrix Calculus: Rank and Decomposition

Covers matrix rank, determinant, and decomposition in linear algebra.

Eigenvalues and Eigenvectors in 3D

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