Khan Academy Static

As we'll see in this tutorial, it is hard not to love a basis where all the vectors are orthogonal to each other and each have length 1 (hey, this sounds pretty much like some coordinate systems you've known for a long time!). We explore these orthonormal bases in some depth and also give you a great tool for creating them: the Gram-Schmidt Process (which would also be a great name for a band).

6997_Projections_onto_subspaces_with_orthonormal_bases.html

7000_Orthogonal_matrices_preserve_angles_and_lengths.html

6999_Example_using_orthogonal_change_of_basis_matrix_to_find_transformation_matrix.html

7001_The_Gram_Schmidt_process.html

6995_Introduction_to_orthonormal_bases.html

6996_Coordinates_with_respect_to_orthonormal_bases.html

7002_Gram_Schmidt_process_example.html

7003_Gram_Schmidt_example_with_3_basis_vectors.html

6998_Finding_projection_onto_subspace_with_orthonormal_basis_example.html