Symmetric and Anti-symmetric Matrices

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Description

This lecture covers the concepts of symmetric and anti-symmetric matrices, defining their properties and providing examples. It also discusses matrix powers, the inverse of a matrix, elementary matrices, and the utility of the transpose. The instructor explains how to determine if a matrix is invertible and the role of elementary operations in matrix manipulation.

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related lectures (26)

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In course

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related lectures (26)

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Matrix Operations: Rules and Applications

Covers matrix operations, including multiplication, transposition, powers, and inverses, and explains how to determine if a matrix is invertible.

Matrix Operations: Inverse and Reduction to Echelon Form

Covers matrix operations and reduction to echelon form with practical examples.

Linear Algebra: Matrices and Operations

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

Elementary Matrices and Inverses

Covers elementary matrices, their properties, and the algorithm to find the inverse of a matrix.