Monthly Archives: April 2017

Notes on the t-distribution

Posted on April 26, 2017 by mg50

Let X1,X2,…,Xn be IID normal variables with mean μ and variance σ2. Let X― be the mean of these variables, and define the deviations Di=X―–Xi. 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′=limf(x+a,y)–f(x,y)a=∂g∂x+i∂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 v1,…,vn 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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