File:Generalized inverse subspaces-right.svg
Size of this PNG preview of this SVG file: 389 × 599 pixels. Other resolutions: 156 × 240 pixels | 311 × 480 pixels | 498 × 768 pixels | 664 × 1,024 pixels | 1,329 × 2,048 pixels | 512 × 789 pixels.
Original file (SVG file, nominally 512 × 789 pixels, file size: 38 KB)
This is a file from the Wikimedia Commons. Information from its description page there is shown below.
Commons is a freely licensed media file repository. You can help.
Commons is a freely licensed media file repository. You can help.
Summary
| Description |
English: Visualize a right inverse X of a matrix A, both viewed as linear maps between the vector spaces U and V. A is surjective, and X maps A's image to a complement subspace of its kernel bijectively. If the complement is the orthogonal complement, then X is the Moore–Penrose inverse.
Here, “K∁ is a complement subspace of K” means that their direct sum spans the whole space, yet they intersect only at the zero vector. |
| Date | |
| Source | Own work |
| Author | David, but not Hilbert |
| Other versions |
|
| SVG development |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:44, 9 December 2025 | | 512 × 789 (38 KB) | David, but not Hilbert | Uploaded own work with UploadWizard |
File usage
The following page uses this file:
