Foundations-of-Applied-Mathematics / lab-issue-tracker

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FourierTransform: Vector is missing spacing/commas #120

Open Abelpalmer22 opened 1 day ago

Abelpalmer22 commented 1 day ago

Typo Details:

Are these supposed to have commas between the entries? Right now it looks like multiplication

Suggested Fix:

Just add commas between them

Source Lines

Relevant segments in `/Volume2/FourierTransform/FourierTransform.md`:
- Approximate line: 215:
  - Section: The Discrete Fourier Transform:
    - TeX: $\w_n^{(k)} = \begin{bmatrix}\omega_n^0  \omega_n^{-k}  \cdots  \omega_n^{-(n-1)k}\end{bmatrix}\trp ,$ (`\w_n^{(k)} = \begin{bmatrix}\omega_n^0  \omega_n^{-k}  \cdots  \omega_n^{-(n-1)k}\end{bmatrix}\trp ,`)
- Approximate line: 230:
  - Section: The Discrete Fourier Transform:
    - TeX: $\begin{split}
F_{n} = \frac{1}{n} \begin{bmatrix}\w_n^0  \w_n^1  \w_n^2  \cdots  \w_n^{n-1} \end{bmatrix}
= \frac{1}{n}\left[\begin{array}{*{5}c} 
1 & 1 & 1 & \cdots & 1 \\
1 & \omega_n^{-1} & \omega_n^{-2} & \cdots & \omega_n^{-(n-1)} \\
1 & \omega_n^{-2} & \omega_n^{-4} & \cdots & \omega_n^{-2(n-1)} \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
1 & \omega_n^{-(n-1)} & \omega_n^{-2(n-1)} & \cdots & \omega_n^{-(n-1)^2}
\end{array}\right],
\end{split}$ (`\begin{split}
F_{n} = \frac{1}{n} \begin{bmatrix}\w_n^0  \w_n^1  \w_n^2  \cdots  \w_n^{n-1} \end{bmatrix}
= \frac{1}{n}\left[\begin{array}{*{5}c} 
1 & 1 & 1 & \cdots & 1 \\
1 & \omega_n^{-1} & \omega_n^{-2} & \cdots & \omega_n^{-(n-1)} \\
1 & \omega_n^{-2} & \omega_n^{-4} & \cdots & \omega_n^{-2(n-1)} \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
1 & \omega_n^{-(n-1)} & \omega_n^{-2(n-1)} & \cdots & \omega_n^{-(n-1)^2}
\end{array}\right],
\end{split}`)
iso2013 commented 23 hours ago

Typo Details:

Commas should go between entries in the vector

Suggested Fix:

Commas in the vector

Source Lines

Relevant segments in `/Volume2/FourierTransform/FourierTransform.md`:
- Approximate line: 296:
  - Section: The Fast Fourier Transform:
    - TeX: $\f\odot\g = \begin{bmatrix}f_0g_0  f_1g_1  \cdots  f_{n-1}g_{n-1}\end{bmatrix}\trp ,$ (`\f\odot\g = \begin{bmatrix}f_0g_0  f_1g_1  \cdots  f_{n-1}g_{n-1}\end{bmatrix}\trp ,`)