Questions tagged [vector-space]

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What is a "continuous vector"?

I have seen the concept of a "continuous vector" described in the context of embeddings. For instance, this answer to a question on embeddings in the context of deep learning. I obviously ...
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How the vector-space isomorphism between $\mathbb{R}^{m \times n}$ and $\mathbb{R}^{mn}$ guarantees reshaping matrices to vectors?

Consider the following paragraph from section 5.4 Gradients fo Matrices of the chapter Vector Calculus from the textbook titled Mathematics for Machine Learning by Marc Peter Deisenroth et al. Since ...
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What is the role of left singular vectors in SVD?

SVD decomposition of a data matrix $A$ of order $n \times d$ and rank $r$ can be expressed as follows $$A_{n\times d} = U_{n\times r}D_{r \times r}V^{T}_{r \times d}$$ The rows of the data matrix $A$ ...
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