Questions tagged [vector-space]

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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 $A$ ...