A search may need values, coordinates, or an ordering. These are different outputs. Decide which one you need before choosing where, nonzero, argsort, or searchsorted...
Joining arrays is a modeling choice. Does the new data add observations, add features to existing observations, or add a new experiment axis? Those choices call for different shapes, even when all inputs contain the same number of elements...
Reshaping preserves the number of elements...
For A ∈ ℝ^(m×n), x ∈ ℝⁿ, and b ∈ ℝ^m...
Indexing answers two questions: which values are selected, and whether the selection shares storage with the original. The second question determines whether a later assignment changes your input...
An array has three separate properties: its shape says how values are indexed, its dtype says how each value is represented, and its data contains the values. Choosing the wrong dtype can change an answer even when the shape is right...
A real matrix A ∈ ℝ^(m×n) maps n-component input vectors to m-component output vectors. The formula...
A statistic summarizes the data you actually have. A probability model describes how data might be generated. A sample's mean is not required to equal its model's mean, and changing an axis, denominator, or weighting rule can change which quantity you are computing...
A real coordinate vector v = (v₀,…,vₙ₋₁) is an ordered list of n components. A NumPy array of shape (n,) is a convenient representation, but NumPy's shape rules are part of the calculation: they are not mathematical row/column notation inferred from how an array is printed...