### Questions (36)

 30 What is the proof that covariance matrices are always semi-definite? 26 Affine transformation applied to a multivariate Gaussian random variable - what is the mean vector and covariance matrix of the new variable? 12 Could we show $1-(x-\frac{x^3}{3!}+\frac{x^5}{5!}-\dots)^2=(1-\frac{x^2}{2!}+\frac{x^4}{4!}- \dots)^2$ if we didn't know about Taylor Expansion? 11 Solving matrix equations of the form $X = AXA^T + C$ 11 What is the general formula for calculating dot and cross products in spherical coordinates?

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 35 What is the proof that covariance matrices are always semi-definite? 28 Affine transformation applied to a multivariate Gaussian random variable - what is the mean vector and covariance matrix of the new variable? 27 Find five positive integers whose reciprocals sum to $1$ 18 Integration by substitution, why do we change the limits? 11 How to check if a point is inside a rectangle?

### Tags (82)

 36 matrices × 10 28 multivariable-calculus × 6 35 probability × 6 28 normal-distribution × 4 35 proof-writing × 5 28 random-variables × 4 35 vector-spaces × 2 28 linear-algebra × 4 35 positive-semidefinite × 2 27 calculus × 2