Singular Values Calculator
Calculate the singular values of a matrix using power iteration method.
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Singular Values
The singular values of a matrix A are the square roots of the eigenvalues of A*A:
\[ \sigma_i = \sqrt{\lambda_i(A^*A)} \]
Properties:
- Always non-negative
- Ordered from largest to smallest
- Number equals min(rows, cols)
- Related to matrix norm
- Used in SVD decomposition
Calculation Methods:
- Power Iteration
- QR Algorithm
- Lanczos Method
Applications:
- Principal Component Analysis (PCA)
- Image compression
- Data dimensionality reduction
- Signal processing
- Machine learning
Geometric Interpretation:
- Stretching factors
- Measure of matrix rank
- Condition number
- Stability indicator