mittenullsingulaarväärtuste

Mittenullsingulaarväärtuste, often abbreviated as NSV, refers to the non-zero singular values obtained from the Singular Value Decomposition (SVD) of a matrix. Singular Value Decomposition is a fundamental matrix factorization technique that decomposes any matrix into three other matrices. These singular values are a sequence of non-negative real numbers that represent the "strength" or importance of different dimensions within the data represented by the matrix.

When performing SVD, a matrix A is decomposed as A = UΣV^T, where U and V are orthogonal matrices, and Σ is a diagonal matrix containing the singular values on its main diagonal, typically arranged in descending order. The non-zero singular values are particularly significant because they indicate the rank of the matrix and the number of linearly independent rows or columns.

The concept of mittenullsingulaarväärtuste is crucial in various applications, including dimensionality reduction techniques like Principal Component Analysis (PCA). By retaining only the largest singular values and their corresponding components, one can construct a lower-rank approximation of the original matrix that captures most of its variance. This process helps in noise reduction, data compression, and improving the efficiency of algorithms by working with a smaller, more manageable representation of the data. The number of these non-zero singular values directly corresponds to the intrinsic dimensionality of the data.