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  3. Sylvester's law of inertia - Wikipedia

    en.wikipedia.org/wiki/Sylvester's_law_of_inertia

    A symmetric matrix can always be transformed in this way into a diagonal matrix which has only entries ⁠ ⁠, ⁠ + ⁠, ⁠ ⁠ along the diagonal. Sylvester's law of inertia states that the number of diagonal entries of each kind is an invariant of ⁠ A {\displaystyle A} ⁠ , i.e. it does not depend on the matrix S {\displaystyle S} used.

  4. Sylvester equation - Wikipedia

    en.wikipedia.org/wiki/Sylvester_equation

    The answer is that these two matrices are similar exactly when there exists a matrix X such that AX − XB = C. In other words, X is a solution to a Sylvester equation. This is known as Roth's removal rule. [4] One easily checks one direction: If AX − XB = C then

  5. Euler's equations (rigid body dynamics) - Wikipedia

    en.wikipedia.org/wiki/Euler's_equations_(rigid...

    Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L.

  6. Metal matrix composite - Wikipedia

    en.wikipedia.org/wiki/Metal_matrix_composite

    In materials science, a metal matrix composite (MMC) is a composite material with fibers or particles dispersed in a metallic matrix, such as copper, aluminum, or steel. The secondary phase is typically a ceramic (such as alumina or silicon carbide ) or another metal (such as steel [ 1 ] ).

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  8. Screw axis - Wikipedia

    en.wikipedia.org/wiki/Screw_axis

    The Boerdijk–Coxeter helix is an example of a screw axis symmetry that is nonperiodic.. A screw displacement (also screw operation or rotary translation) is the composition of a rotation by an angle φ about an axis (called the screw axis) with a translation by a distance d along this axis.

  9. Mortgage and refinance rates for Oct. 24, 2024: Average rates ...

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    The consumer price index released on October 10 showed inflation cooling to its lowest level since February 2021, with a 2.4% year-over-year increase in consumer prices in September, down from 2.5 ...