Locutusque/TinyMistral-248M-v2
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TITLE: Prove that I -xx* is singular if and only x*x = 1
QUESTION [0 upvotes]: (=>) Suppose I - xx* is singular if and only there is a y such that (I−xx*)y=0, i.e. xx* y=y. Now set λ=x* y. Then y=λx, i.e. xx* λx=λx
Thus λx(x* x) = λx => x* x = 1
(<=) Suppose x*x = 1
Please help
REPLY [1 votes]: Just start from the b... | 203,149 |
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This fits well with what I wrote last week on the same subject.
The big question of course is how you measure the success of such campaigns, and how you compare one t... | 152,081 |
\begin{document}
\begin{frontmatter}
\author{Mahouton Norbert Hounkonnou\corref{cor1}${}^1$}
\cortext[cor1]{norbert.hounkonnou@cipma.uac.bj}
\author{Sama Arjika\corref{cor2}${}^1$}
\cortext[cor2]{rjksama2008@gmail.com}
\author{ Won Sang Chung\corref{cor3}${}^2$ }
\cortext[cor3]{mimip4444@hanmail.net}
\title{\bf N... | 137,553 |
\begin{document}
\hbox{}
{\parindent=0pt
{\large \bf Lagrangian and Hamiltonian dynamics of
submanifolds}
\bigskip
{\bf G.Giachetta}, {\bf L.Mangiarotti}$^1$, {\bf G.Sardanashvily}$^2$
\bigskip
\begin{small}
$^1$ Department of Mathematics and Informatics, University of
Camerino, 62032 Camerino (MC), Italy
\meds... | 203,228 |
\begin{document}
\title[On Foreman's maximality principle]{On Foreman's maximality principle}
\author[Mohammad Golshani and Yair Hayut]{Mohammad
Golshani and Yair Hayut}
\thanks{The first author's research was in part supported by a grant from IPM (No. 91030417).}
\begin{abstract}
In this paper we consider For... | 127,727 |
TITLE: All-pairs shortest paths in trees?
QUESTION [12 upvotes]: This is a reference request, since I'm sure what follows isn't new, but I can't seem to find it.
Suppose that we have a finite tree $T$ with non-negative weights on the edges. Naively, computing the path lengths (i.e., sum of the weights along the unique... | 88,404 |
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TITLE: Complex normal coordinates in Kähler manifolds
QUESTION [6 upvotes]: Let $(M, g, J, \omega)$ be a Kähler manifold. That is, $(M, J)$ is a complex manifold, $g$ is a Hermitian metric on $M$ and
$$\omega (X, Y) = g(JX, Y)$$
is a closed two form.
As a Riemannian manifold $(M, g)$, for each $x\in M$, one can find a ... | 64,018 |
\begin{document}
\begin{center}
{\large\bf A $p$-adic analogue of Chan and Verrill's formula for $1/\pi$}
\end{center}
\vskip 2mm \centerline{Ji-Cai Liu}
\begin{center}
{\footnotesize Department of Mathematics, Wenzhou University, Wenzhou 325035, PR China\\
{\tt jcliu2016@gmail.com } \\[10pt]
}
\end{center}
\vskip... | 104,268 |
Xped has developed a number of technologies that simplify how devices are on-boarded.
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In this section, we take a closer look at the geometry of $\mathfrak X$, and compare it with related moduli spaces.
\subsection{Comparison of $\mathfrak{X}$ with the spaces of weighted admissible covers $\overline{\mathcal{H}}_4^3(1/6+\epsilon)$}
Recall that $\overline{\mathcal H}_4^3(1/6 + \epsilon)$ is the moduli sp... | 141,173 |
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TITLE: Proof of Cancellation Law for Multiplication in N (Induction)
QUESTION [2 upvotes]: I'm struggling a bit to prove the Cancellation Law for multiplication for the Natural numbers, using induction.
So far I have this:
Having $a, b \in N$ e $S = \lbrace c \in N | a \cdot c = b \cdot c \longrightarrow a = b \rbrace... | 107,848 |
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Monday, June 25, 2018
The new OneIT Strategic Plan details strategic goals OneIT will pursue in support of the institutional mission, and how OneIT will evolve to meet technology needs now and in the future. Drafting the plan was a highly collaborative effort that involved significant engagement of campus stakeholders,... | 92,937 |
Item #: AB-GR
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YAML Metadata Warning:The task_categories "text2text-generation" is not in the official list: text-classification, token-classification, table-question-answering, question-answering, zero-shot-classification, translation, summarization, feature-extraction, text-generation, fill-mask, sentence-similarity, text-to-speech, text-to-audio, automatic-speech-recognition, audio-to-audio, audio-classification, audio-text-to-text, voice-activity-detection, depth-estimation, image-classification, object-detection, image-segmentation, text-to-image, image-to-text, image-to-image, image-to-video, unconditional-image-generation, video-classification, reinforcement-learning, robotics, tabular-classification, tabular-regression, tabular-to-text, table-to-text, multiple-choice, text-ranking, text-retrieval, time-series-forecasting, text-to-video, image-text-to-text, image-text-to-image, image-text-to-video, visual-question-answering, document-question-answering, zero-shot-image-classification, graph-ml, mask-generation, zero-shot-object-detection, text-to-3d, image-to-3d, image-feature-extraction, video-text-to-text, keypoint-detection, visual-document-retrieval, any-to-any, video-to-video, other
Dataset used to train TinyMistral-248m-v2. Consists of around 8 million examples. Consists of the following sources:
- 4 million Wikipedia pages
- 1 million arxiv papers
- 1.5 million web pages sourced from RefinedWeb and SlimPajama
- 200,000 college text books
- 1 million stack exchange forum posts.
This dataset can contain NSFW examples, use at your own risk.
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