The Tabular Matrix Problems via Pseudoinverse Estimation (TMPinv) is a two-stage estimation method that reformulates structured table-based systems - such as allocation problems, transaction matrices, and input-output tables - as structured least-squares problems. Based on the Convex Least Squares Programming (CLSP) framework, TMPinv solves systems with row and column constraints, block structure, and optionally reduced dimensionality by (1) constructing a canonical constraint form and applying a pseudoinverse-based projection, followed by (2) a convex-programming refinement stage to improve fit, coherence, and regularization (e.g., via Lasso, Ridge, or Elastic Net).