Change of basis - ML & AI Coding

36. Change of basis

easy

General

senior

Implement change of basis for a vector, which lets you express the same geometric vector using different coordinate systems. You’ll compute the coordinates of a vector in a new basis using a basis matrix.

[v]_{B} = B^{-1} v

Requirements

Implement the function

python

Rules:

Treat B as a matrix whose columns are the basis vectors.
Compute the new coordinates using a linear solve (preferred) or matrix inverse.
Return the result as a NumPy array.
Do not use any helper libraries beyond NumPy and Python built-ins.
Assume B is invertible.

Example

python

Output:

python

Input Signature

Argument	Type
B	np.ndarray
v	np.ndarray

Output Signature

Return Name	Type
value	np.ndarray

Constraints

Use np.linalg.solve; avoid explicit inverse.
Return NumPy array.
B is (n,n) invertible; v length n.

Hint 1

Treat the columns of B as basis vectors. The new coordinates x satisfy B @ x = v.

Hint 2

Avoid forming B^{-1} explicitly. Use np.linalg.solve(B, v) to compute x more stably.

Hint 3

Convert inputs to NumPy arrays with dtype=float (if not already), solve for x, then return x directly.

Roles

ML Engineer

AI Engineer

Companies

General

Levels

senior

entry

Input Arguments

Edit values below to test with custom inputs

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