On Ubuntu 20.10, just:
ffmpeg -i input.mp4 -vf "subtitles=subtitle.srt" output.mp4
To change font size: stackoverflow.com/questions/21363334/how-to-add-font-size-in-subtitles-in-ffmpeg-video-filter
ffmpeg -i input.mp4 -vf "subtitles=subtitle.srt:force_style='Fontsize=64'" output.mp4
The default appears to be 24, so just multiply that by whatever seems like a reasonable factor.
Note howver that .ass subtitle files can contain style information, which ffmpeg respects. Aegisub can produce and preview such styles, making .ass one of the best options.
Unlike the simple case of a matrix, in infinite dimensional vector spaces, the spectrum may be continuous.
The quintessential example of that is the spectrum of the position operator in quantum mechanics, in which any real number is a possible eigenvalue, since the particle may be found in any position. The associated eigenvectors are the corresponding Dirac delta functions.
Minkowski space by Ciro Santilli 37 Updated 2025-07-16
with a weird dot product-like operation called the Minkowski inner product.
Because the Minkowski inner product product is not positive definite, the norm induced by an inner product is a norm, and the space is not a metric space strictly speaking.
The name given to this type of space is a pseudometric space.
Reproductive cue by Ciro Santilli 37 Updated 2025-07-16
A signal that indicates that an animal is ready for mating.
Asianometry by Ciro Santilli 37 Updated 2025-07-16
Very good channel to learn some basics of semiconductor device fabrication!
Focuses mostly on the semiconductor industry.
youtu.be/aL_kzMlqgt4?t=661 from Video "SMIC, Explained by Asianometry (2021)" from mentions he is of Chinese ascent, ancestors from Ningbo. Earlier in the same video he mentions he worked on some startups. He doesn't appear to speak perfect Mandarin Chinese anymore though based on pronounciation of Chinese names.
asianometry.substack.com/ gives an abbreviated name "Jon Y".
Video 1.
Reflecting on Asianometry in 2022 by Asianometry (2022)
Source. Mentions his insane work schedule: 4 hours research in the morning, then day job, then editing and uploading until midnight. Appears to be based in Taipei. Two videos a week. So even at the current 400k subs, he still can't make a living.
Personalized learning by Ciro Santilli 37 Updated 2025-07-16
Inferior compared to self-directed learning, but better than the traditional "everyone gets the same" approach.
Video 1.
Project SOCRATES at Illinois University Urban-Champaign (1966)
Source. It is 2020, and we are not there yet. God!
TODO: use the results from the quantum harmonic oscillator solution to precisely illustrate the discussion at Schrödinger picture with a concrete example.
As always, the best way to get some intuition about an equation is to solve it for some simple cases, so let's give that a try with different fixed potentials.

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