Question

Write a function Topic that accepts three arguments, U,D and Vt U,D and Vt are Numpy arey which the singular value decomposition of a matrix Xᵀ which is a centred data matrix. The NumPy array D is a full matric (not just a vector of the singular values). Geli returns a data matrix Yᵀ which is the corresponding matrix of principal components of X⁷

Answer 1

The topic of this question is Linear Algebra and the function described uses the singular value decomposition (SVD) to calculate the principal components of a data matrix.

Step-by-step explanation:

The topic of this question is Linear Algebra.

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any m x n matrix via an extension of the polar decomposition. The SVD represents an expansion of the original matrix into a sum of three simpler matrices: a unitary matrix, a diagonal matrix, and another unitary matrix.

The function described in the question accepts three arguments: U, D, and Vt. U and Vt are unitary matrices and D is a diagonal matrix containing the singular values. The function returns a data matrix Y that corresponds to the principal components of the original data matrix X.