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arkadiusz-jadczyk.eu | ||
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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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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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www.sirver.net
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| | | | | [AI summary] The article explains the geometric interpretation of the least squares problem using linear algebra concepts like projection and column spaces. | |
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djalil.chafai.net
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| | | This post is devoted to few convex and compact sets of matrices that I like. The set \( {\mathcal{C}_n} \) of correlation matrices. A real \( {n\times n} \) matrix \( {C} \) is a correlation matrix when \( {C} \) is symmetric, semidefinite positive, with unit diagonal. This means that \[ C_{ii}=1, \quad C_{ji}=C_{ji},\quad \left\geq0 \] for every \(... | ||
