Abstract
Let \(\mathcal{L}\) be a linear space, \({\mathcal{L}}_{1}\) be a linear subspace of \(\mathcal{L}\) and A be a linear operator in \(\mathcal{L}\). In general, for any vector \(\mathbf{x} \in {\mathcal{L}}_{1}\), A x may not belong to \({\mathcal{L}}_{1}\).
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Notes
- 1.
Let us note for a reader who is not familiar with partial derivatives that the coefficients of the linear combinations ϕ i are calculated by the following rule: the coefficient of x 1 in ϕ i is equal to the coefficient of x i 2 in Φ while the coefficient of x j for j≠i is equal to the coefficient of x i x j in Φ divided by two.
- 2.
James Joseph Sylvester (1814–1897) was famous English and American mathematician of nineteenth century.
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© 2011 Springer-Verlag Berlin Heidelberg
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Aleskerov, F., Ersel, H., Piontkovski, D. (2011). Eigenvectors and Eigenvalues. In: Linear Algebra for Economists. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20570-5_9
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DOI: https://doi.org/10.1007/978-3-642-20570-5_9
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