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Give a square matrix its eigenvalues - #2064
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A matrix had a characteristic polynomial (#1625) and no eigenvalues. Matrix.Eigenvalues is the set of its roots in a variable of its own, solved by the equation solver: radicals up to the fourth degree, and past it where the polynomial factors. The characteristic polynomial divides by nothing, so the roots carry no condition an elimination's pivots would bring: [[0, J], [J, 0]] has sqrt(J^2) and -sqrt(J^2), which hold at J = 0 too. A repeated root is one member of the set; a matrix that is not square has none. The MCP server solved the characteristic polynomial itself, waiting for this; am_eigenvalues now takes the library's, and its README lists the workarounds that remain. Fixes #1676. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…trix # Conflicts: # Sources/MCP/README.md
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Fixes #1676.
Matrix.Eigenvaluesis the set of the characteristic polynomial's roots, in a variable of the matrix's own, solved by the equation solver. That means radicals up to the fourth degree, and beyond it wherever the polynomial factors.[[0, J], [J, 0]]hassqrt(J^2)and-sqrt(J^2), which hold atJ = 0too.null.am_eigenvaluesnow uses the library's property, and the README lists the workarounds that remain.EigenvaluesTestcovers a symmetric 3×3 ({1, 2, 11}), a repeated root, the symbolic matrix above with noprovided, and a non-square matrix. It also checks three 2×2 matrices, one with complex eigenvalues, by makingA - λIsingular for each eigenvalue. The full unit suite passes (16,710), and so do the MCP tests (325). The library builds for netstandard2.0. This is a pure addition,PublicApi.txtgains one line, and no answer changes, so it has no BREAKING-CHANGES entry. The MCP README's list of workarounds is edited by #2061, #2062 and #2063 as well, so whichever merges later has a one-line conflict there.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura