Abstract algebra | Linear algebra
In mathematics, and more specifically in abstract algebra, an element x of a *-algebra is self-adjoint if . A self-adjoint element is also Hermitian, though the reverse doesn't necessarily hold. A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, if then since in a star-algebra, the set {x,y} is a self-adjoint set even though x and y need not be self-adjoint elements. In functional analysis, a linear operator on a Hilbert space is called self-adjoint if it is equal to its own adjoint A∗. See self-adjoint operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is self-adjoint if and only if the matrix describing A with respect to this basis is Hermitian, i.e. if it is equal to its own conjugate transpose. Hermitian matrices are also called self-adjoint. In a dagger category, a morphism is called self-adjoint if ; this is possible only for an endomorphism . (Wikipedia).
A particularly awful aspect of self-hatred is that we may not even be aware that we are suffering from it. Here is a list of questions to help us diagnose an absence of self-compassion. Sign up to our mailing list to receive 10% off your first order with us: https://r1.dotdigital-pages.com
From playlist SELF
It’s all too easy to be extremely tough on ourselves; we need – at points – to get better at self-compassion. Here is an exercise in how to lessen the voices of self-flagellation. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/dJJMFS FURTHER READING
From playlist SELF
To have sound levels of self-esteem is one of the gateways to happiness. But achieving this has very little to do with the progress of our careers. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/1Uj9JM Watch more films on SELF: http://bit.ly/TSOLself P
From playlist SELF
How to Be More Straightforward
We prefer people who are ‘straightforward’: who are direct and unambiguous about their desires and characters. Becoming more so involves untangling the self-deceptions we constructed when we were young. Sign up to our mailing list to receive 10% off your first order with us: https://r1.do
From playlist SELF
If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.
From playlist Self-Driving Cars
How Unloving Parents Generate Self-Hating Children
Our sense of self-worth is dependent upon the love we were shown as children. The legacy of an unloving parent may be a lifetime of self-hatred, which we need to unpick in order to escape. Sign up to our mailing list to receive 10% off your first order with us: https://r1.dotdigital-pages.
From playlist SELF
Open Source & Feelings 2015 - From the Inside Out: How Self-Talk Affects Your Community
From the Inside Out: How Self-Talk Affects Your Community by Kat Toomajian Identifying and discouraging negative self-talk is a simple thing, but it can have a huge impact on your community in a positive way. It increases self-confidence, improves morale, and generally results in happier,
From playlist Open Source & Feelings 2015
Why You Should Read Self-help Books
We're often encouraged to be dismissive of the idea of self-help books, but reading in order to grow emotionally is one of the most serious and important of all literary tasks. For gifts and more from The School of Life, visit our online shop: https://goo.gl/NrBA4D Join our mailing list: h
From playlist SELF
In Praise of Introspective People
However healthy it often is to try to fit in and assume we must just be like everyone else, there are also benefits in sometimes accepting that we might in the end not be and this needn’t be a cause of concern or shame. Sign up to our mailing list to receive 10% off your first order with
From playlist SELF
Self-adjoint operators. All eigenvalues of a self-adjoint operator are real. On a complex vector space, if the inner product of Tv and v is real for every vector v, then T is self-adjoint.
From playlist Linear Algebra Done Right
Positive operators. Square roots of operators. Characterization of positive operators. Each positive operator has a unique positive square root.
From playlist Linear Algebra Done Right
Lara Ismert: "Heisenberg Pairs on Hilbert C*-modules"
Actions of Tensor Categories on C*-algebras 2021 "Heisenberg Pairs on Hilbert C*-modules" Lara Ismert - Embry-Riddle Aeronautical University, Mathematics Abstract: Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenber
From playlist Actions of Tensor Categories on C*-algebras 2021
Normal operators. Characterization of normal operators by ||Tv|| = ||T*v|| for all v. Eigenvectors of a normal operator corresponding to distinct eigenvalues are orthogonal.
From playlist Linear Algebra Done Right
Kristin Courtney: C*-structure on images of completely positive order zero maps
Talk by Kristin Courtney in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on September 16, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Andy Wathen: Parallel preconditioning for time-dependent PDEs and PDE control
We present a novel approach to the solution of time-dependent PDEs via the so-called monolithic or all-at-once formulation. This approach will be explained for simple parabolic problems and its utility in the context of PDE constrained optimization problems will be elucidated. The underlyi
From playlist Numerical Analysis and Scientific Computing
Jens Kaad: Differentiable absorption of Hilbert C*-modules
The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C^*-module is isomorphic to a direct summand in a standard module. In this talk, I will generalize this result by incorporating a densely defined derivation on the base C^*-algebra. The extra com
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Esteban Andruchow: Metric geometry in homogeneous spaces of the unitary group of a C∗-algebra. 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
Automorphic Levi-Sobolev Spaces, Boundary-Value Problems, and Self-Adjoint Operators - Paul Garrett
Paul Garrett University of Minnesota January 31, 2013 Application of Plancherel's theorem to integral kernels approximating compact period functionals yields estimates on (global) automorphic Levi-Sobolev norms of the functionals. The utility of this viewpoint can be illustrated in reconsi
From playlist Mathematics
Thalia Wheatley - What is Self-Awareness?
'Self awareness' has a simple definition: the mental activity that reflects back on itself, the mental process of being aware of oneself being aware. Is self-awareness a uniquely human trait? Some animals seem to disagree. The deep significance of self-awareness is how on earth can physica
From playlist Is Your 'Self' Just an Illusion? - Closer To Truth - Core Topic
Lazaro Recht: Metric geometry in homogeneous spaces of the unitary group of a C* -algebra. 2
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry