Characteristic Polynomial: Definition & Examples

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Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Explores the properties of invertible matrices, including unique solutions and linear independence.

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

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Covers the concept of polynomial characteristic of a matrix and its relation to eigenvalues.

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.