Similar matrices have the same characteristic polynomial

Comments · 28

• HO

  @holyshit922 · 1 year ago (edited)

  If you continue your series of videos about algebra you could record something on orthogonalization <br>1. Give us definition of dot product (or rather inner product)<br>2. Tell us something on Gram - Schmidt orthogonlization process<br>3. Tell us sometinng on rotation and reflection matrices <br>4. Present us QR decomposition

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• JA

  @jamesharmon4994 · 2 years ago

  This went SO far over my head that I need a telescope!!

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• RY

  @RyanLewis-Johnson-wq6xs · 2 years ago

  This is excellent vocabulary and math.

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• RY

  @RyanLewis-Johnson-wq6xs · 2 years ago

  You’re amazing!

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• PU

  @punditgi · 2 years ago

  The characteristic of a Prime Newtons video is that it is chock full of useful information about math similar to the best teachers on YouTube. 😢😊

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• AC

  @Achieve-and-win · 1 year ago

  I really thankfull to you ,while teaching with smile and happy &nbsp;gives a great impact on me .

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• HO

  @holyshit922 · 2 years ago (edited)

  Fact that similar matrices have the same eigenvalues is used in numerical linear algebra to find eigenvalues <br>There are used transformations which preserve similarity like Householder reflections or Givens rorations or just modification of Gaussian elimination<br>To preserve similarity we must perform elementary operations on both rows and columns

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• RY

  @RyanLewis-Johnson-wq6xs · 2 years ago (edited)

  Characteristic Polynomial:determinANT(A-λ I) &nbsp;Char. Poly: det(A-λI)=0

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• AH

  @ahmedali6519 · 1 year ago

  thankss

• AN

  @Anmol_Sinha · 2 years ago

  What does drawing the square in the end mean?

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• CL

  @Clemm_mm · 2 years ago

  Nice

• RY

  @RyanLewis-Johnson-wq6xs · 2 years ago

  PBP^-1-P λIP^-1=P(BP^-1-λIP^-1) &nbsp; A-λI=P(B-λI)P^-1 &nbsp; det(A-λI)=det(P(B-λI)P^-1)=detP*det(B-λI)*detP^-1

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