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Lecture
Determinant of a Matrix
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Matrix Calculus
Covers the definition and basic operations of matrices, including addition, scalar multiplication, and matrix multiplication.
Elementary Matrices and Inverses
Covers elementary matrices, their properties, and the algorithm to find the inverse of a matrix.
Diagonalization of Symmetric Matrices
Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.
Diagonalization Cream: Distinct Eigenvalues
Covers the diagonalization of matrices with distinct eigenvalues and the importance of this process.
Symmetric Matrices: Diagonalization
Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.
Matrix Operations: Definitions and Properties
Covers the definitions and properties of matrices, including matrix operations and determinants.
Diagonalizable Matrices: Properties and Examples
Explores the properties and examples of diagonalizable matrices, emphasizing the relationship between eigenvectors and eigenvalues.