• Title: Sylvester’s Law of Inertia

• Series: Sylvester’s Law of Inertia

• YouTube-Title: Sylvester’s Law of Inertia

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• Subtitle on GitHub: syl01_sub_eng.srt missing

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• Definitions in the video: sesquilinear form, quadratic form, Hermitian

• Related videos:

  • Hilbert Spaces 6 | Orthogonal Complement
• Timestamps

  00:00 Introduction

  00:30 Example of quadratic form

  01:30 Definition (sesquilinear form)

  04:25 Definition quadratic form

  05:15 Polarization identity

  06:40 Matrix representation of quadratic form

  09:58 Diagonalization of quadratic form

  11:30 Proof of diagonalization

  18:36 Decomposition of vector space

  21:00 Theorem: Sylvester’s law of inertia

  22:12 Proof of theorem

  24:59 Credits

• Subtitle in English (n/a)
• Quiz Content (n/a)

• Date of video: 2026-08-23

• Last update: 2026-08

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