Symmetric Matrices and Positive Definiteness

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MIT 18.06SC Linear Algebra, Fall 2011
Instructor: David Shirokoff

A teaching assistant works through a problem on symmetric matrices and positive definiteness.

License: Creative Commons BY-NC-SA
  1. MIT OpenCourseWare
  2. linear algebra
  3. symmetric matrices
  4. positive definiteness
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Комментарии
Автор

He is actually using the more formal definition of positive definite matrices, which is that for any x, (x bar transpose) * A * x must be greater than zero
this definition isn't taught in the lecture but it is good to know.

magicandmagik
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Part A possible alternate solution?
A is positive definite and every positive definite matrix has all positive eigenvalues

If det(A) = 0 then 0 is an eigenvalue of the matrix, but this is a contradiction because positive definite matrix must have positive eigenvalues. This shows det(A) is non-zero.

magicbanana
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Why are symmetric matrices always diagonalizable?

garethcheung
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3:49 Why does a projection matrix's eigenvalues are either 0 or 1?

ysmashimaro
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Help, every time he says "detA" I hear "daddEY", then he started with "detS" and all i hear "datAss"☠️

danicarovo