Row echelon form: Difference between revisions

Revision as of 23:46, 7 November 2023

Revision as of 23:56, 7 November 2023

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:<math> \tilde{V}_i = \text{span}\{e_n, \dots, e_{n-i+1}\}, \quad i =1, \dots n. </math>

Then <math>X_\lambda(\mathcal{V}) \subset \mathbf{Gr}_k(V) </math> consists of those <math>k</math>-dimensional subspaces <math>w \subset V</math> that have a basis <math>(W_1\tilde{W}_1, \dots, W_k\tilde{W}_k)</math>

consisting of elements

:: <math>W_i\tilde{W}_i \in \tilde{V}_{n- L_i +1}=\tilde{V}_{k+\lambda_i -i +1 }, \quad i=1, \dots, k </math>

of the subspaces <math>\{\tilde{V}_{k+\lambda_i -i +1}\}_{i=1, \dots, k} </math> (which, relative to the standard basis, are the row vectors <math>(W_k, \dots, W_1)</math> of the row echelon form, written in reverse order.)

==Notes==