File:Change-of-basis coordinate mapping (matrix representation).png
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Summary
| Description |
English: This diagram illustrates the relationship between coordinate vectors in different bases in ℝ².
A vector x is shown in the standard basis (e₁, e₂) and in another basis (a₁, a₂). The matrix A = [a₁ | a₂], whose columns are the basis vectors expressed in standard coordinates, maps coordinate vectors x_A in the basis (a₁, a₂) to standard coordinates x via x = A x_A. The left panel shows the standard coordinate grid, while the right panel shows the coordinate system defined by the basis (a₁, a₂). The same vector is represented in both coordinate systems. This figure provides a geometric interpretation of the change-of-basis relation x_old = A x_new. |
| Date | |
| Source | Own work |
| Author | Eteri byazrova (GraphMath) |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:06, 30 March 2026 | | 2,240 × 2,180 (342 KB) | wikimediacommons>Eteri byazrova | Uploaded own work with UploadWizard |
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