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Catalyst University
Postulates of Quantum Mechanics: Orthonormality & Basis Sets
Postulates of Quantum Mechanics: Orthonormality & Basis Sets
Curated Video
Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Orthonormal Basis
In this video, we will cover Orthonormal Basis.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and...
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and...
Khan Academy
Khan Academy: Linear Algebra: Introduction to Orthonormal Bases
Video defining an orthonormal set as a set of vectors that all have the length of 1 and are orthogonal to each other. Using proof by contradiction, the set is proven to be linearly independent and can be considered an orthonormal basis....
Khan Academy
Khan Academy: Linear Algebra: The Gram Schmidt Process
Video about the Gram-Schmidt process which is used to create an orthonormal basis from any basis. First an orthonormal basis is created in one dimension by normalizing the vector and then in two dimensions by building on the...
Khan Academy
Khan Academy: Linear Algebra: Projection Onto Subspace With Orthonormal Basis Ex
Video defining a specific orthonormal basis and using the simplified formula found in the previous video to calculate the projection of a vector onto a subspace with the given orthonormal basis. [6:42]
Khan Academy
Khan Academy: Linear Algebra: Coordinates With Respect to Orthonormal Bases
Video showing that the standard basis is an example of an orthonormal basis. Explains how orthonormal bases make good coordinate systems since they make it easy to find coordinates. A general orthonormal basis is defined and then it is...
Khan Academy
Khan Academy: Linear Algebra: Gram Schmidt Process Example
Video using the Gram-Schmidt process to create an orthonormal basis from a specific basis with two basis vectors for a given plane. [13:14]
Khan Academy
Khan Academy: Linear Algebra: Projections Onto Subspaces With Orthonormal Bases
Video giving another reason why orthonormal bases are useful. First reviews how to find the projection of a vector onto a subspace and then describes how an orthonormal basis can be used to find the projection. Simplifies the...
Khan Academy
Khan Academy: Linear Algebra: Gram Schmidt Example With 3 Basis Vectors
Video using the Gram-Schmidt process to create an orthonormal basis from a specific basis with three basis vectors in four-dimensional space. [13:57]
Khan Academy
Khan Academy: Using Orthogonal Change of Basis Matrix
Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set.
Khan Academy
Khan Academy: Orthonormal Basis: The Gram Schmidt Process
This video is about the Gram-Schmidt process which is used to create an orthonormal basis from any basis.
Khan Academy
Khan Academy: Finding Projection Onto Subspace With Orthonormal Basis Example
This video shows an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.
Khan Academy
Khan Academy: Orthonormal Basis: Coordinates With Respect to Orthonormal Bases
Video showing that orthonormal bases make for good coordinate systems. A general orthonormal basis is defined and then it is shown how to write a general vector x with respect to the orthonormal basis.
Khan Academy
Khan Academy: Orthonormal Basis: Gram Schmidt Process Example
Video using the Gram-Schmidt process to create an orthonormal basis from a specific basis with two basis vectors for a given plane.
Khan Academy
Khan Academy: Projections Onto Subspaces With Orthonormal Bases
A video about projections onto subspaces with orthonormal bases.
Khan Academy
Khan Academy: Orthonormal Basis: Orthogonal Matrices Preserve Angles and Lengths
This is a video showing that orthogonal matrices preserve angles and lengths.
Khan Academy
Khan Academy: Orthonormal Basis: Gram Schmidt Example With 3 Basis Vectors
Video using the Gram-Schmidt process to create an orthonormal basis from a specific basis with three basis vectors in four-dimensional space.