query: A question about the Littlewood-Paley decomposition.
positive_passages.docid: 23520
positive_passages.text: A property of Littlewood-Paley decomposition
negative_passages.docid: 91627
negative_passages.text: What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$?
negative_passages.docid: 64741
negative_passages.text: The square root of positive definite matrix
negative_passages.docid: 35625
negative_passages.text: Direct sum of orthogonal subspaces
negative_passages.docid: 75225
negative_passages.text: Exercise $ 3.4.15 $ of David Marker’s “Model Theory”.
negative_passages.docid: 55621
negative_passages.text: Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
negative_passages.docid: 146801
negative_passages.text: Primary decomposition of an ideal
negative_passages.docid: 28155
negative_passages.text: Two questions about diagonalization
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 33423
negative_passages.text: Decomposition of semisimple Lie algebra via its roots
negative_passages.docid: 116632
negative_passages.text: Gram-Schmidt in Hilbert space?
negative_passages.docid: 157751
negative_passages.text: Relationship between Partial Harmonic Sum and Logarithm.
negative_passages.docid: 98225
negative_passages.text: Dimensions with Rank-Nullity question
negative_passages.docid: 40858
negative_passages.text: Multiplicative nature of the separability degree
negative_passages.docid: 30060
negative_passages.text: Decomposing the normal distribution
negative_passages.docid: 88820
negative_passages.text: Three linked question on non-negative definite matrices.
negative_passages.docid: 100899
negative_passages.text: Coefficients of the characteristic polynomial