"to save their lives" is a little dramatic, considering they were in a closed tech interview. I'm sure if you gave them 20 seconds on the internet (you know, the resource they would have in a real life problem solving situation) they could find one.

My graduate adviser use to say, if you ask "how do you add 1+1?" a student with a bachelor's degree answers "2". A person with a master's degree will write a 10 line C program to calculate it, then tell you "2". A person with a PhD just says "I don't know, but I can tell you where to find the answer."

Hmmm... I don't think I remember how to compute the eigenvectors of a 2x2 matrix, other than constructing a system of linear equations representing the outcome of the matrix multiplication and solving it.

But come on, everyone knows how to use the definition of the standard (l2) vector norm to normalize a vector! Don't joke!

Wouldn't you just take the length of the vector with sqrt(4+9+16) and divide each component by it? Or is this a different kind of 'vector' than graphics people are familiar with?

But Obviously. The same chap can invoke the SparseVector and DenseVector Java APIs from Spark, but doesn't know what a simple unit vector is or how to compute one. I think we are entering into a bleak era where there are umpteen built-in ML APIs for everything under the sun but the engineers who use them have no idea what these things really are - they just invoke the constructor and write some code and think they are now doing ML.

Seems hard to believe that an "engineer" with a degree in engineering or CS wouldn't know what is a unit vector.

Why? There are plenty of directions you can take through a CS degree that will never have you dealing with vectors at all. And subsequently there are plenty of CS heavy careers where you will never deal with it.

What little I remember about vectors is from my high school maths classes, and in my 20 years of doing software engineering it's come up exactly once (for a GIS related project).

You are probably right about CS. I only have experience with engineering and wouldn't expect any engineer (i.e. a major in engineering) to not know that.

I wouldn't expect anyone working with machine learning to not know these concepts either.

Well, um ,a diagonal matrix is already diagonalizaed (lol) so its P marix is {{1,0},{0,1}} and hence the you can use those two as your diagonal entries are the eigenvalues.