For a matrix representing linear homogeneous equations, partial-derivative coefficient determinant {Hessian determinant} indicates inflection points.
Determinants {Jacobian determinant} {functional determinant} can be for coordinate transformations: double integral of F(x,y) * dx * dy = double integral of G(u,v) * determinant(fu, fv, gu, gv) * du * dv. Jacobian determinants have two rows of partial derivatives, one row for F(x,y) and one row for G(u,v). Jacobian determines scalar for unit vectors. Jacobians can determine normal vectors at function intersections.
Product of determinant inverse and second determinant B and first determinant A calculates third determinant C {similar determinant}, which is similar to second determinant: A^-1 * B * A = C.
3-Algebra-Equation-System-Determinant
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Date Modified: 2022.0225