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The inner product of two column vectors \mathbf a and \mathbf b, \mathbf a \cdot \mathbf b, written in matrix form is \mathbf a^T * \mathbf b.
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Definition of Partial Derivative: Correct Form?
- Thread starter Cyrus
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The discussion revolves around the correct definition of the partial derivative, specifically whether it should be represented as a row vector or a column vector. Participants note that the first definition, which presents the partial derivatives as a row vector, is commonly found in textbooks, while the second definition shows them as a column vector. The debate highlights the importance of context in mathematical proofs, as the representation affects the transformation rules for gradients and displacement vectors. It is emphasized that gradients should be treated as row vectors due to their relationship with dual spaces, while displacement vectors are typically column vectors. Ultimately, the consensus leans towards using the definition found in the relevant textbook or class notes for consistency.
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