Gershgorin Circle Theorem: Eigenvalue Localization for Square Matrices

This GeoGebra example demonstrates the Gershgorin circle theorem for square matrices. It visualizes Gershgorin discs—circles centered at diagonal entries of a matrix with radii equal to the sum of absolute values of off-diagonal entries in each row—showing that all eigenvalues of the matrix lie within the union of these discs. Core mathematical concepts include square matrices, diagonal and off-diagonal entries, absolute values, eigenvalue localization, and the Gershgorin circle theorem from linear algebra. The construction uses the GeoGebra Sequence command to generate a collection of circle objects (circs, circs_t), supported by point objects A1, A2, A3, B1, B2, B3, C1, C2, C3 and variables n, sum, sum_t to compute centers and radii dynamically. Suitable for university-level linear algebra courses, matrix analysis, and self-study, this interactive visualization helps learners understand eigenvalue bounds and matrix properties through geometric representation.