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Title: Norms and Banach Spaces
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Series: Functional Analysis
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YouTube-Title: Functional Analysis 6 | Norms and Banach Spaces
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Bright video: https://youtu.be/imYQJOgUx7Y
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Dark video: https://youtu.be/Slmtlv3g0C8
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: fa06_sub_eng.srt missing
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Timestamps
00:00 Introduction
00:33 Definition (norm)
04:17 Normed space
04:50 Connection to metrics
06:00 Banach space
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Subtitle in English (n/a)
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Quiz Content
Q1: What is not a property of a norm?
A1: positive definite
A2: absolutely homogenous
A3: linear
A4: triangle inequality
Q2: Let $X = \mathbb{R}$ the vector space of real numbers. Is the absolute value $|\cdot|$ a norm on $X$?
A1: Yes!
A2: No!
Q3: What is the correct definition of a Banach space?
A1: A normed vector space that is also complex.
A2: A normed vector space that is also real.
A3: A normed vector space that is also complete.
A4: A normed vector space that is also a metric space.