# Eigenvector Orthogonal

This post categorized under Vector and posted on June 11th, 2018.

Overview. Eigenvalues and eigenvectors feature prominently in the vectorysis of linear transformations. The prefix eigen-is adopted from the German word eigen for Normal matrices. A complex normal matrix ( ) has an orthogonal eigenvector basis so a normal matrix can be decomposed as where is a unitary matrix.If further restricted to be a Hermitian matrix ( ) the diagonal matrix has only real values.These vector lectures of Professor Gilbert Strang teaching 18.06 were recorded in Fall 1999 and do not correspond precisely to the current edition of the textbook.

If all eigenvalues are different then plugging these back in gives independent equations for the components of each corresponding eigenvector These vector lectures of Professor Gilbert Strang teaching 18.06 were recorded in Fall 1999 and do not correspond precisely to the current edition of the textbook.

SUMMARY In this article the underlying theory of clinical diffusion MR imaging including diffusion tensor imaging (DTI) and fiber tractography is reviewed. First a brief explanation of the basic physics of diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) mapping is provided.

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