Topic: matrix-manipulation-problem / Level: advanced

• 2001. Write a program to compute the singular value decomposition (SVD) of a matrix and reconstruct it.
• 2002. Write a program to implement the QR decomposition of a matrix using Gram-Schmidt orthogonalization.
• 2003. Write a program to perform matrix factorization for collaborative filtering with alternating least squares.
• 2004. Write a program to compute the matrix exponential using the Padé approximation.
• 2005. Write a program to find the eigenvalues and eigenvectors of a matrix using the power iteration method.
• 2006. Write a program to check if a matrix is diagonally dominant and compute its spectral radius.
• 2007. Write a program to implement the power method for finding the largest eigenvalue of a matrix.
• 2008. Write a program to compute the Moore-Penrose pseudoinverse of a matrix.
• 2009. Write a program to perform Cholesky decomposition of a symmetric positive definite matrix.
• 2010. Write a program to calculate the determinant of a large matrix using LU decomposition.
• 2011. Write a program to perform matrix completion using low-rank approximation.
• 2012. Write a program to implement the Conjugate Gradient method for solving linear systems.
• 2013. Write a program to calculate the Kronecker product of two matrices.
• 2014. Write a program to implement the Bellman-Ford algorithm for finding shortest paths in a weighted graph.
• 2015. Write a program to compute the covariance matrix from a dataset using matrix operations.
• 2016. Write a program to check if a matrix is a block diagonal matrix and compute its determinant.
• 2017. Write a program to implement the fast Fourier transform (FFT) using matrix multiplication.
• 2018. Write a program to calculate the rank of a matrix using its singular values.
• 2019. Write a program to perform multivariate polynomial regression using matrices.
• 2020. Write a program to compute the Hessian matrix of a scalar function using second derivatives.
• 2021. Write a program to implement the regularized regression (Ridge and Lasso) using matrix methods.
• 2022. Write a program to check if a matrix is positive semi-definite using its eigenvalues.
• 2023. Write a program to perform Kernel PCA for non-linear dimensionality reduction.
• 2024. Write a program to calculate the Frobenius norm of a matrix.
• 2025. Write a program to implement the Broydens method for solving non-linear equations using matrices.
• 2026. Write a program to compute the Gini impurity for a dataset represented as a matrix.
• 2027. Write a program to perform spectral clustering using the adjacency matrix of a graph.
• 2028. Write a program to calculate the Jaccard similarity between two sets of points represented as matrices.
• 2029. Write a program to implement the Elkans algorithm for k-means clustering.
• 2030. Write a program to perform the MDS (Multidimensional Scaling) algorithm using a distance matrix.
• 2031. Write a program to compute the partition function for a probabilistic model using matrices.
• 2032. Write a program to check if two matrices are similar using Jordan form.
• 2033. Write a program to perform semi-supervised learning using matrix representations.
• 2034. Write a program to implement the K-nearest neighbors algorithm using KD-trees for efficient searching.
• 2035. Write a program to compute the support vector regression (SVR) using kernel methods.
• 2036. Write a program to calculate the confusion matrix for multi-class classification using matrices.
• 2037. Write a program to implement the Kalman filter for estimating the state of a dynamic system using matrices.
• 2038. Write a program to check if a matrix is an idempotent matrix (A² = A).
• 2039. Write a program to perform time series forecasting using ARIMA and GARCH models with matrices.
• 2040. Write a program to compute the leverage scores from a linear regression model using matrices.
• 2041. Write a program to implement the Expectation-Maximization (EM) algorithm for Gaussian Mixture Models.
• 2042. Write a program to calculate the Chi-square statistic using matrices for categorical data.
• 2043. Write a program to implement the k-medoids clustering algorithm using distance matrices.
• 2044. Write a program to compute the marginal distribution from a joint probability distribution matrix.
• 2045. Write a program to perform Bayesian inference using matrices.
• 2046. Write a program to implement the maximum entropy model using matrices.
• 2047. Write a program to compute the total variation distance between two probability distributions using matrices.
• 2048. Write a program to check if a matrix is a valid probability distribution.
• 2049. Write a program to implement the Fuzzy C-means clustering algorithm.
• 2050. Write a program to compute the optimal transport plan between two distributions using the Wasserstein metric.

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