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Math Linear algebra Alternate coordinate systems (bases) Orthonormal bases and the Gram-Schmidt process

Orthonormal bases and the Gram-Schmidt process

    • Introduction to orthonormal bases
      This is the currently selected item.
    • Coordinates with respect to orthonormal bases
    • Projections onto subspaces with orthonormal bases
    • Finding projection onto subspace with orthonormal basis example
    • Example using orthogonal change-of-basis matrix to find transformation matrix
    • Orthogonal matrices preserve angles and lengths
    • The Gram-Schmidt process
    • Gram-Schmidt process example
    • Gram-Schmidt example with 3 basis vectors
    Next lesson
    Eigen-everything
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Math·Linear algebra·Alternate coordinate systems (bases)·Orthonormal bases and the Gram-Schmidt process

Introduction to orthonormal bases

Orthonormal bases and the Gram-Schmidt process

    • Introduction to orthonormal bases
      This is the currently selected item.
    • Coordinates with respect to orthonormal bases
    • Projections onto subspaces with orthonormal bases
    • Finding projection onto subspace with orthonormal basis example
    • Example using orthogonal change-of-basis matrix to find transformation matrix
    • Orthogonal matrices preserve angles and lengths
    • The Gram-Schmidt process
    • Gram-Schmidt process example
    • Gram-Schmidt example with 3 basis vectors
    Next lesson
    Eigen-everything
Coordinates with respect to orthonormal bases
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Coordinates with respect to orthonormal bases