Monthly Archives: April 2017

Notes on the t-distribution

Posted on April 26, 2017 by mg50

Let $X_1, X_2, \ldots, X_n$ be IID normal variables with mean $\mu$ and variance $\sigma^2$. Let $\overline{X}$ be the mean of these variables, and define the deviations $D_i = \overline{X} – X_i$. Let $Y = [X_1 \ X_2 \ \ldots … Continue reading →

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Complex analysis notes

Posted on April 16, 2017 by mg50

Cauchy-Riemann Let $f(z) = f(x + iy) = g(x, y) + ih(x, y)$. If it’s holomorphic, we can differentiate along the real line and the imaginary line: $f’ = \lim\frac{f(x + a, y) – f(x, y)}{a} = \frac{∂g}{∂x} + i\frac{∂h}{∂x}$ $f’ = … Continue reading →

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Invariant Subspaces

Posted on April 13, 2017 by mg50

Let M be a matrix, and suppose $v_1, \ldots, v_n$ for a basis for a linearly independent subspace of M. This means $$ Mv_1 = a_{11}v_1 + a_{12}v_2 + \ldots + a_{1n}v_n \\ Mv_2 = a_{21}v_1 + a_{22}v_2 + \ldots … Continue reading →

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