If what you say [whatever you mean by it] is true, then the same thing can be said about Euclidean diagrams [as projections of a 4d-space?]. I had two diagrams (projections of worldlines with respect to different rest frames) which contained invariant elements. Inspecting the diagrams di...
Also, I was reading the next section and it mentions that Einstein's equation is invariant, it gives the Einstein equations in the form . Does this mean applying transformation laws to either side will yield the same equation (which is actually covariance, I think? I've never been good at...
What does Injective mean in math? In mathematics, an injective function (also known as injection, or one-to-one function) isa function f that maps distinct elements to distinct elements; that is, f(x1) = f(x2) implies x1= x2. In other words, every element of the function's codomain...
By averaging the above dilation lemma, we can also establish a “structure theorem” that decomposes the indicator function of into components, each of which are invariant with respect to a certain shift in . We can establish this theorem in the case of measure-preserving actions on probability...
It is now tempting to try to set up an approximately scale-invariant blowup solution. It seems that the first step in this is to construct a “soliton” type localized steady state solution, that is a solution , to the equation that decays in the variable; one can then hope to do a...
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Chapter 43/ Lesson 1 146K Learn what translation, rotation, and reflection mean in math. Identify examples of these transformations and discover the key differences between them. Explore our homework questions and answers library Search...
If you are wondering “If smaller angles mean two vectors are more similar, why are we not just using the angles - why all this complicated math?”, we will be answering that later on! The Significance of Cosine Similarity in Data Analysis and NLP ...
It is now tempting to try to set up an approximately scale-invariant blowup solution. It seems that the first step in this is to construct a “soliton” type localized steady state solution, that is a solution , to the equation that decays in the variable; one can then hope to do a...
This is consistent with the random matrix theory interpretation, since is also the spectral measure of , where is the orthogonal projection to the span of the first basis elements, so in particular has spectral measure . If is unitarily invariant then (by a fundamental result of Voiculescu) ...