>>14362436They do? Lambda is a real number.
All it's saying is that the product of a random vector by a random number is still a vector, and that in fact, it's just the original vector scaled by lambda.
They define it right there, , that's the only property of lambda, it's just a random real number. Don't think about similarity to other symbols such as how lambda is often used to depict eigenvalues, and pay attention to the definitions.
>>14361606It really is just algebra for the first part. Log of a product is the sum of the logs.
Then the 1st term does not depend on , so the
>I guess the upside triangle is a gradient(?)Yes, for a function f of n variables,
, so denotes the k-th entry,
>It's not clear what these mean when are togetherDerivative of the sum is the sum of the derivatives.
Pi Product and Sigma Summation notation is just a compact way of writting a product and sum, it's just a for loop if you're familiar with programming.
