MATH-111(e): Linear Algebra

Lectures in this course (136)

Explores vector spaces, linear independence, and bases, illustrating their importance through examples in R2 and R3.

Explores the equality between Ker A and Ker (ATA) in linear algebra.

Explores the diagonalizability of matrices based on eigenvalue multiplicities and eigenvectors.

Covers the concept of orthogonal complement and projection in vector spaces.

Introduces algebraic properties, vector equations, and matrix operations.

Explains finding the closest point on a plane using orthogonal projection.

Explores linear applications and their impact on vector space independence.

Explains linear combinations, vector equations, matrix equations, and systems of equations in vector form.

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Explores vector approximation and distance calculation through exercises and solutions, focusing on orthogonal projections and vector spaces.

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

Covers the properties of orthogonal matrices and their eigenvalues.

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

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

Covers the analysis of electric cable potential based on temperature data.

Explains orthogonal bases, angles between vectors, and uniqueness of coefficients.

Explores the properties of orthonormal vectors in Euclidean space through key equations and demonstrations.

Explores orthogonal families, vector orthogonality, and linear combinations in vector spaces.

Explores properties of determinants, invertibility criteria, and geometric interpretations for matrices.

Explores orthogonal projection calculation and orthonormal bases uniqueness through matrix operations.

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