MATLAB Tensor Examples with Implementation Approaches

This example showcases tensor operations implemented in MATLAB. Tensors, as fundamental constructs in high-dimensional linear algebra, represent multidimensional arrays capable of encoding vectors, matrices, and higher-order data structures. They play critical roles across mathematics, physics, and engineering disciplines. The implementation demonstrates practical MATLAB techniques including: using ndarray functions for tensor creation, employing tensor multiplication algorithms via pagemtimes, and implementing tensor decomposition methods like CANDECOMP/PARAFAC (CP) using the n-way toolbox. Key functions highlighted include reshape for dimension manipulation, kron for Kronecker products, and einsum-like operations using nested loops for custom contractions. This example provides hands-on experience in tensor computation workflows, from basic operations to advanced applications in data analysis and multilinear algebra. For enthusiasts of numerical linear algebra, these implementations offer insights into efficient tensor handling using MATLAB's matrix-based paradigm with optimized memory management for large-scale multidimensional data.