Involutory matrix

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

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

Covers the main theorem of linear algebra and the conditions for injectivity.

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

Explores the reduction of a matrix based on its eigenvalues, focusing on the case of two real eigenvalues.

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Explores the criterion for matrix invertibility and the calculation of the inverse.

Explores canonical transformations, symplectic groups, real matrices, preserved quantities, and volumes in phase space.

Explores least squares in linear regression, hypothesis testing, outliers, and model assumptions.

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.