Linear Algebra: Orthogonality and Diagonalization

This final course in the Johns Hopkins sequence focuses on perpendicularity and its consequences. Dot products and orthogonal bases support projections and least-squares problems, then lead to symmetric matrices and quadratic forms. It is a useful comparison for learners who can already compute with matrices and now want to understand approximation geometrically.

What you will learn

• Construct an orthogonal basis with Gram–Schmidt.
• Interpret least squares as an orthogonal projection.
• Connect symmetric matrices with orthogonal eigenvectors.

Who this suits

Choose this after introductory matrix algebra, eigenvalues and vector spaces. It is intermediate material despite some familiar-looking arithmetic.

Before you enroll

An exact linear solution and a least-squares approximation answer different questions. Check that you can explain the residual before relying on a software solution.

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Put it into practice

Fit a line to three points that do not lie on one line. Calculate the residual and demonstrate its orthogonality to the model’s column space.

Source and review

This overview is based on the provider's published information, checked on 12 October 2026. It is an editorial assessment, not a claim that we completed the resource. Time filters are approximate study ranges; projects and exercises can take longer.

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