Solving Polynomial Equations: Basics and Applications

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Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

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

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

Covers the definition and properties of determinants, including the rule of Sarrus for 3x3 matrices.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

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

Covers matrices, linear applications, vector spaces, and bijective functions.

Covers the properties and calculations of the determinant of a matrix.

Explores the exponential of a matrix, properties, Frobenius norm, nilpotent matrices, commutativity, and system solutions.