Hereditary is a 2018 American supernatural psychological horror drama film written and directed by Ari Aster, in his feature directorial debut. It stars Toni Collette, Alex Wolff, Milly Shapiro and Gabriel Byrne as a family haunted by a mysterious presence after the death of their secretive grandmother.
Hereditary premiered on January 21, 2018, in the Midnight section at the 2018 Sundance Film Festival, and was theatrically released in the United States on June 8, 2018. It was acclaimed by critics, with Collette’s performance receiving particular praise, and was a commercial success, making over million on a million budget to become A24’s highest-grossing film worldwide Video Rating: / 5
Finite-dimensional C*-algebras and their (unital) *-homomorphisms are introduced. The main examples are introduced beginning with function spaces over finite sets to direct sums of matrix algebras.
Notes:
1. I forgot to mention that the involution * is conjugate-linear (instead of linear).
2. When I say a *-homomorphism preserves all the algebra structure, I mean it’s an algebra homomorphism (it’s linear and preserves products), it preserves *, and it preserves the unit. However, the norm need not be preserved. There are *-homomorphisms that can decrease the norm (but they cannot increase it!). Nevertheless, any injective *-homomorphism is an isometry (this is proved in Dixmier’s book on C*-algebras).
3. I said that 1 does not equal 0 in the definition of a C*-algebra, but you don’t want that restriction. Indeed, the set of functions on the empty set is a perfectly fine C*-algebra and corresponds to 0 (in fact, any algebra over the complex numbers where 0=1 is isomorphic this one). One thing to note about this is that there are NO (unital) homomorphisms from this one to a non-zero algebra. However, the 0 algebra is terminal as there is a unique homomorphism from any algebra into it.
4. Finally, I also forgot to write U* on the right-hand-side of the last example.
Reference: Attal’s book “Lectures in Quantum Noise Theory” (http://math.univ-lyon1.fr/~attal/chapters.html), specifically Lecture 6, reviews many of these things in detail and with greater generality.
Another reference: Chapter 2 of https://arxiv.org/abs/1708.00091
This is part of a series of lectures on special topics in linear algebra. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming’s error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.
These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room. Video Rating: / 5
In our first lecture, we introduce the category of C*-algebras, within which our course will take place. Video Rating: / 5
I tested a bunch of pregnancy tests to figure out which one detects early pregnancy first and which ones fail. I am testing 6dp5dt or 11DPO after a frozen embryo transfer. This would have been the equivalent of 3 days before my missed period and was 6 days before my 12 day post transfer blood work.
Odds of a positive pregnancy test by DPO: https://www.countdowntopregnancy.com/pregnancy-test/results-by-day-past-ovulation.php
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