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Material Detail

Best Solution and Ordinary Least Squares

Best Solution and Ordinary Least Squares

This resource presents the least squares solution as a geometric projection onto the column space of a matrix. Given a system Ax = b with no exact solution, the best approximation is obtained by projecting b onto col(A).

The decomposition b = b∥ + b⊥ is illustrated visually, where b∥ lies in col(A) and b⊥ is orthogonal to it. The solution minimizes the error ‖Ax − b‖ and provides a geometric foundation for linear regression and data...

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Keywords:
orthogonal projection, data fitting, Ax = b, normal equations, best approximation, least squares, column space, linear regression, linear algebra
Disciplines:
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More about this material

Material Type:
Reference Material
Date Added to MERLOT:
March 23, 2026
Date Modified in MERLOT:
March 23, 2026
Authors:
 
 
Submitter:
Eteri Byazrova
Primary Audience:
College General Ed, College Lower Division, College Upper Division
Technical Format:
PDF, Website
Mobile Compatibility:
Not specified at this time
Language:
English
Cost Involved:
No
Source Code Available:
No
Creative Commons:
Unknown

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