query: find the dimension of $W.$
positive_passages.docid: 157109
positive_passages.text: Finding the Dimension of a Matrix Polynomial: $W$ = { $p(B)$ : $p$ is a polynomial with real coefficients}
negative_passages.docid: 6547
negative_passages.text: Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
negative_passages.docid: 3810
negative_passages.text: When is a function a dimension?
negative_passages.docid: 125184
negative_passages.text: Why $\dim(\hom(V,W))=\dim(V) * \dim(W)$?
negative_passages.docid: 152742
negative_passages.text: Finding a basis of an infinite-dimensional vector space?
negative_passages.docid: 59864
negative_passages.text: Find the area of the following
negative_passages.docid: 76188
negative_passages.text: Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
negative_passages.docid: 107987
negative_passages.text: How do I calculate $u(w)=\int_0^\infty \frac{1-\cos(wt)}{t}\,e^{-t}\,dt$?
negative_passages.docid: 149634
negative_passages.text: $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
negative_passages.docid: 54032
negative_passages.text: dimensional analysis - how to find the dimensions of a variable inside an angle
negative_passages.docid: 143929
negative_passages.text: dimension of a connected Manifold
negative_passages.docid: 104578
negative_passages.text: Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
negative_passages.docid: 141794
negative_passages.text: Invariant subspaces of specific dimension
negative_passages.docid: 28520
negative_passages.text: Exponential or logarithm of a dimensionful quantity?
negative_passages.docid: 156727
negative_passages.text: A step in the proof of Characterization of $W^{1,\infty}$
negative_passages.docid: 41520
negative_passages.text: Prove that $L(V,W)$ forms a vector space
negative_passages.docid: 73286
negative_passages.text: Show that the set of all symmetric, real matrices is a subspace, determine the dimension