Question

For various values of the integers $m$ and $n$, compare the spectra of $A A^t$ and $A^t A$, where $\mathrm{A}=\operatorname{rand}(\mathrm{n}, \mathrm{m})$. Justify the observations.

    For various values of the integers $m$ and $n$, compare the spectra of $A A^t$ and $A^t A$, where $\mathrm{A}=\operatorname{rand}(\mathrm{n}, \mathrm{m})$. Justify the observations.
Numerical Linear Algebra
Numerical Linear Algebra
Grégoire Allaire,… 1st Edition
Chapter 2, Problem 19 ↓
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For various values of the integers $m$ and $n$, compare the spectra of $A A^t$ and $A^t A$, where $\mathrm{A}=\operatorname{rand}(\mathrm{n}, \mathrm{m})$. Justify the observations.
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Transcript

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0:00 Hello.
00:01 So here we're going to let a matrix a be an m by n matrix.
00:07 Okay, so then we have that a transpose then is going to be an n by n, n by m matrix.
00:15 So we have then that a transpose.
00:17 If a is m by n, then a transpose is going to be n by m.
00:22 So n rows and m columns.
00:26 Okay.
00:27 So we have then...
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