Linear Algebra: For the real symmetric matrix [3 2 / 2 3], 1) verify that all eigenvalues are real, 2) show that eigenvectors for distinct eigenvalues are orthogonal with respect to the standard inner product, and 3) find an orthogonal matrix P such that P^{-1}AP = D is diagonal. The Spectral Theorem states that every symmetric matrix can be put into real diagonal form using an orthogonal change of basis matrix (or there is an orthonormal basis of eigenvectors).

Tagged under: Mathematics,linear,algebra,symmetric,matrix,diagonal,orthogonal,change,basis,orthonormal,eigenvector,eigenvalue,null,space,spectral,theorem

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

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Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

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Dr Ayla Göl
@iladylayla

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