Why the determinant tells you about volume scaling under a linear transformation

What the rank-nullity theorem says: rank(A) + nullity(A) = n for an m×n matrix

Rank-nullity theorem: Rank(A) + Nullity(A) = Number of columns (n) in A

Why L1 distance is called Manhattan distance — grid-like paths

L1 distance mimics grid-like city blocks, hence "Manhattan" distance

Why the L1 unit ball is a diamond shape and the L2 unit ball is a circle

L1 norm: Manhattan distance, L2 norm: Euclidean distance

How does the curse of dimensionality affect the performance and accuracy of clustering algorithms in high-dimensional datasets?

High-dimensional data can lead to sparse clusters, reducing clustering accuracy due to increased distance between points

Why most transformer operations are memory-bound, not compute-bound

Transformer operations rely heavily on matrix multiplications, which are memory-intensive tasks

How does the choice of norm affect the shape of the unit ball in a given vector space, specifically comparing the properties of L1 and L∞ norms?

L1 norms create diamond-shaped unit balls, while L∞ norms yield cube-shaped unit balls