Easy

Gram Matrix (AᵀA)

Easy

~12 min

code completion

The Gram Matrix

The Gram matrix of a matrix A is defined as:

G = A^{⊤} A

This appears throughout ML:

In the normal equation for linear regression:

(A^{⊤} A)^{- 1} A^{⊤} y

In kernel methods and covariance matrices

In PCA (related to the covariance matrix)

In NumPy:

G = A.T @ A

Your task:

Implement gram_matrix(A) that computes $A^{⊤} A$ .

Example Tests

Identity input gives identity output

Input: {"A":[[1,0],[0,1]]}

Expected: [[1,0],[0,1]]

3x2 matrix gives 2x2 Gram matrix

Input: {"A":[[1,2],[3,4],[5,6]]}

Expected: [[35,44],[44,56]]

Result is always square (n x n)

Input: {"A":[[1,2,3],[4,5,6]]}

Expected: [3,3]

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