Hackers' Pub

Syntax	Description	Examples
`"` keyword `"`	Finds the string within quotes, including spaces. Case-insensitive. (Escape quotes inside with `\"`)	`"Hackers' Pub"`
`from:` handle	Finds content written by the specified user.	`from:hongminhee` `from:hongminhee@hollo.social`
`lang:` ISO 639-1	Finds content written in the specified language.	`lang:en`
`#` tag	Finds content with the specified tag. Case-insensitive.	`#HackersPub`
condition condition	Finds content that satisfies both conditions on either side of the space (logical AND).	`"Hackers' Pub" lang:en`
condition `OR` condition	Finds content that satisfies at least one of the conditions on either side of the OR operator (logical OR).	`#HackersPub OR "Hackers' Pub" lang:en`
`(` condition `)`	Combines the operators within the parentheses first.	`(#HackersPub OR "Hackers' Pub" OR "Hackers Pub") lang:en`

robinhouston @robinhouston@mathstodon.xyz

1/4/2026, 12:31:25 AM

Public

Imagine reading this if you didn't know what a reflection was.

(This is not a criticism, just a thought that amused me.)

1.1 Reflections Recall what is meant by a reflection in a (real) euclidean space V endowed with a positive definite symmetric bilinear form (λ, μ). A reflection is a linear operator s on V which sends some nonzero vector α to its negative while fixing pointwise the hyperplane H_α orthogonal to α. We may write s = s_α, bearing in mind however that s_α = S_cα for any nonzero c ∈ ℝ. There is a simple formula: s_α λ = λ - (2(λ, α) / (α, α)) α.

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