Some comments about measures, Jacobians and Moore-Penrose inverse

11/05/2019

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Some general problems of Jacobian computations in non-full rank matrices are discussed in this work. In particular, the Jacobian of the Moore-Penrose inverse derived via matrix differential calculus is revisited. Then the Jacobian in the full rank case is derived under the simple and old theory of the exterior product.

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Some comments about measures, Jacobians and Moore-Penrose inverse

The tensor rank of 5x5 matrices multiplication is bounded by 98 and its border rank by 89

Inverse properties of a class of seven-diagonal (near) Toeplitz matrices

Approximating inverse FEM matrices on non-uniform meshes with H-matrices

On the Boomerang Uniformity of Permutations of Low Carlitz Rank

A Rank-Preserving Generalized Matrix Inverse for Consistency with Respect to Similarity

Simple single-scale microstructures based on optimal rank-3 laminates

The c-differential behavior of the inverse function under the EA-equivalence

Some comments about measures, Jacobians and Moore-Penrose inverse

Related Research

The tensor rank of 5x5 matrices multiplication is bounded by 98 and its border rank by 89

Inverse properties of a class of seven-diagonal (near) Toeplitz matrices

Approximating inverse FEM matrices on non-uniform meshes with H-matrices

On the Boomerang Uniformity of Permutations of Low Carlitz Rank

A Rank-Preserving Generalized Matrix Inverse for Consistency with Respect to Similarity

Simple single-scale microstructures based on optimal rank-3 laminates

The c-differential behavior of the inverse function under the EA-equivalence