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arkadiusz-jadczyk.eu | ||
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nhigham.com
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| | | | | For an $latex n\times n$ matrix $latex \notag A = \begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix} \qquad (1) $ with nonsingular $latex (1,1)$ block $LATEX A_{11}$ the Schur complement is $LATEX A_{22} - A_{21}A_{11}^{-1}A_{12}$. It is denoted by $LATEX A/A_{11}$. The block with respect to which the Schur complement is taken need... | |
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stephenmalina.com
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| | | | | Selected Exercises # 5.A # 12. Define $ T \in \mathcal L(\mathcal P_4(\mathbf{R})) $ by $$ (Tp)(x) = xp'(x) $$ for all $ x \in \mathbf{R} $. Find all eigenvalues and eigenvectors of $ T $. Observe that, if $ p = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 $, then $$ x p'(x) = a_1 x + 2 a_2 x^2 + 3 a_3 x^3 + 4 a_4 x^4. | |
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codethrasher.com
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| | | | | A linear mapping from a vector space to a field of scalars. In other words, a linear function which acts upon a vector resulting in a real number (scalar) \begin{equation} \alpha\,:\,\mathbf{V} \longrightarrow \mathbb{R} \end{equation} Simplistically, covectors can be thought of as "row vectors", or: \begin{equation} \begin{bmatrix} 1 & 2 \end{bmatrix} \end{equation} This might look like a standard vector, which would be true in an orthonormal basis, but it is not true generally. | |
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fa.bianp.net
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| | | Six: All of this has happened before. Baltar: But the question remains, does all of this have to happen again? Six: This time I bet no. Baltar: You know, I've never known you to play the optimist. Why the change of heart? Six: Mathematics. Law of averages. Let a complex ... | ||
