https://leanprover-community.github.io/blog/enContents © 2026 <a href="mailto:">The Lean prover community</a> Fri, 17 Jul 2026 16:34:01 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rsshttps://leanprover-community.github.io/blog/posts/semilinear-maps/Frédéric Dupuis<div><p>Since linear maps appear everywhere in mathematics, it comes as no surprise that they have been part of mathlib for quite some time. However, as we were working on adding the basics of functional analysis to mathlib, a drawback quickly became apparent: conjugate-linear maps could not directly be expressed as linear maps. This meant that some constructions could not be formulated in their most natural way: for example, the map that takes an operator to its adjoint on a complex Hilbert space is a conjugate linear map, and so is the Riesz representation that maps a vector to its dual. This was also preventing us from developing the orthogonal group, the unitary group, etc, properly.</p> <p><a href="https://leanprover-community.github.io/blog/posts/semilinear-maps/">Read more…</a> (4 min remaining to read)</p></div>https://leanprover-community.github.io/blog/posts/semilinear-maps/Sat, 11 Dec 2021 11:00:00 GMT