Beeline Algebra with Cogwheel Equations Amalgamate Beeline Cogwheel Equations Diagonalization

 11 July 16:05   First of all (and affectionate of accessible appropriate by the title), mathbf haveto be diagonalizable. Second, the eigenvalues and eigenvectors of mathbf are foudn, and anatomy the cast mathbf which is an augemented cast of eigenvectors, and mathbf which is a cast consisting of the agnate eigenvalues on the capital askew in the aforementioned cavalcade as their agnate eigenvectors. Then with our axial problem:

    mathbf = mathbf + mathbf(t)

    We substitute:

    mathbf = mathbf + mathbf(t)

    Then larboard accumulate by mathbf^

    mathbf = mathbf^mathbf + mathbf^mathbf(t)

    As a aftereffect of Beeline Algebra we yield the afterward identity:

    mathbf = mathbf^mathbf

    Thus:

    mathbf = mathbf + mathbf^mathbf(t)

    And because of the attributes of the askew the problem is a alternation of apparent accustomed cogwheel equations which can be apparent for mathbf and acclimated to acquisition out mathbf.