Linear Equations: Vectors and Matrices

Related lectures (25)

Page 2 of 3

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Explores linear dependence and independence of vectors in geometric spaces.

Covers matrix equations as linear combinations, vector spaces, and geometric interpretations.

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

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Covers the fundamentals of linear equations, matrices, and systems of linear equations, including matrix operations and solutions.

Explores linear systems solutions, vector equations, and equality between vectors.