Quadratic forms | Matrix theory | Theorems in linear algebra

Sylvester's law of inertia

Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of basis. Namely, if A is the symmetric matrix that defines the quadratic form, and S is any invertible matrix such that D = SAST is diagonal, then the number of negative elements in the diagonal of D is always the same, for all such S; and the same goes for the number of positive elements. This property is named after James Joseph Sylvester who published its proof in 1852. (Wikipedia).

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This video tutorial provides a basic introduction into inertia. Inertia is the property of an object to resist changes in its state of motion. According to Newton's First Law of motion, objects at rest tend to stay at rest and objects in motion tend to stay in motion unless acted on by a n

From playlist MECHANICS

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From playlist Mechanics

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From playlist Newton's Laws Video Tutorial Series

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From playlist Julius Sumner Miller - Full Physics Laboratory Demonstrations

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From playlist PHYSICS 12 MOMENT OF INERTIA

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From playlist New Physics Video Playlist

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From playlist PHYSICS 12 MOMENT OF INERTIA

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From playlist Gene Golub SIAM Summer School Videos

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Visit http://ilectureonline.com for more math and science lectures! In this video I will find the moment of inertia of a box. Next video in the moment of inertia series: http://youtu.be/FKyBL1LLz_4

From playlist PHYSICS 12 MOMENT OF INERTIA

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From playlist CALCULUS 3 CH 10 TENSORS

Related pages

Symmetric matrix | Quadratic form | Cholesky decomposition | Coefficient matrix | Metric signature | Diagonal matrix | Morse theory | Change of basis | Conjugate transpose | Invariant (mathematics) | James Joseph Sylvester | Real number | Kernel (linear algebra) | Theorem | Hermitian matrix | Haynsworth inertia additivity formula | Alexander Ostrowski