'Homogeneous linear system' diaporamas de présentation

Application of modern tools for the thermo-acoustic study of annular combustion chambers

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HOMOGENEOUS LINEAR SYSTEMS

HOMOGENEOUS LINEAR SYSTEMS. Up to now we have been studying linear systems of the form We intend to make life easier for ourselves by choosing the vector to be the z ero-vector. We write the new, easier equation in the three familiar equivalent forms: Long-hand:

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A matrix equation has the same solution set as the vector equation which has the same solution set as the linear system

REVIEW. A matrix equation has the same solution set as the vector equation which has the same solution set as the linear system whose augmented matrix is. Therefore: A x = b has a solution if and only if b is a linear combination of columns of A. REVIEW. Theorem 4:

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Chapter 6 Eigenvalues and Eigenvectors

Chapter 6 Eigenvalues and Eigenvectors. 6.1 Definitions. Definition 1: A nonzero vector x is an eigenvector (or characteristic vector ) of a square matrix A if there exists a scalar ? such that Ax = ? x . Then ? is an eigenvalue (or characteristic value ) of A .

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