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📅 May 4, 2026 👤 scraface

May 04, 2026

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📝 Recent Posts

Let \(\mathbf{u} \cdot \mathbf{w} = x\). We aim to maximize \(x\) subj...
\mathbf{u} \cdot \mathbf{u} = 4,\quad \|\mathbf{v}\|^2 = 9,\quad \|\ma...
\mathbf{u} \cdot \mathbf{v} = 1,\quad \mathbf{v} \cdot \mathbf{w} = 6.
Assume all vectors lie in a 3D subspace. Express \(\mathbf{u}\) and \(...
Let us apply the inequality:
but refine using vector decomposition. Decompose \(\mathbf{w}\) into c...
\mathbf{w} = \mathbf{w}_\parallel + \mathbf{w}_\perp, \quad \mathbf{w}...
\|\mathbf{w}_\perp\|^2 = \|\mathbf{w}\|^2 - \|\mathbf{w}_\parallel\|^2...
Now, \(\mathbf{u} \cdot \mathbf{w} = \mathbf{u} \cdot \mathbf{w}_\para...
Since \(\|\mathbf{u} - \mathbf{u} \cdot \mathbf{v} \mathbf{v}\| \geq 0...

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