Define algebraic multiplicity and geometric multiplicity of, Basic Computer Science

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Define algebraic multiplicity and geometric multiplicity of

1. What is the spectrum of a matrix?

2. Define algebraic multiplicity and geometric multiplicity of eigenvalues.

3. What is a diagonalizable matrix?

4. How is the norm of a vector related to the absolute value of a scalar?

5. Prove that for any given vector, ||x||1 ≥ ||x||2.

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