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Repeated eigenvalues
If a matrix has repeated eigenvalues, the eigenvectors of the matched repeated eigenvalues become one of eigenspace. For example, the …
Last updated on
Sep 9, 2022
1 min read
Math
Spectral decomposition
Gaussian kernel matrix can be factorized into \((\Phi \textbf{X})^\textbf{H} \Phi \textbf{X} =\textbf{X}^\textbf{H} \Phi^\textbf{H} …
Last updated on
May 8, 2022
1 min read
Machine learning
,
Math
z-Transformation
The infinite impulse response is a property of a filter of digital signal processing. The filter response of the impulse signal does …
Last updated on
Jun 2, 2022
2 min read
Math
,
Digital signal processing
Cauchy's integral formula and Taylor series
Cauchy’s integral formula defines analytic function evaluation with path integral with denominator translation at evaluation point …
Last updated on
Sep 11, 2021
1 min read
Math
Primitive function
The presence of primitive function is a strong condition that makes a function is analytic in a disc \(D(a,R)\). The meaning is the …
Last updated on
Sep 5, 2021
1 min read
Math
Linear transformation
A norm of linear transformation \(\Lambda : X \rightarrow Y\) is defined by \(\| \Lambda \| = \sup \{ \| \Lambda(x) \|:x \in X, \|x\| …
Last updated on
Mar 3, 2022
1 min read
Math
Convergence
It is the main subject of analysis that finding conditions making sequential mathematical objects like a set, sequence, series to be …
Last updated on
Mar 3, 2022
3 min read
Math
Laplace transformation
The Fourier series represents a periodic function as a descrete vectors. The Fourier transformation turns a time domain non-periodic …
Last updated on
Nov 21, 2020
2 min read
Math
,
Machine learning
Use Korean font in pdf generated from rmarkdown on Windows
yaml --- mainfont: NanumGothic output: pdf_document: latex_engine: xelatex --- The mainfont is the LaTex option. The argument is a font …
Last updated on
Nov 14, 2020
1 min read
R
Convolution and Fourier transformation
Convolution is a vector operation on two vectors. \[ Convolution \\ c * d = d*c \\ (c*d)_n = \Sigma_{i+j} c_i d_j = \Sigma_i c_i …
Last updated on
Oct 23, 2020
1 min read
Math
,
Machine learning
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