Exercise · ZW-DIAGONALIZATION-003 · ★☆☆ Basic
A \(4\times 4\) matrix is diagonalizable. How many linearly independent eigenvectors does it have?
Choose one option.
Show answer
- D. \(4\)
Explanation
Being diagonalizable means having a basis of eigenvectors, and a basis of \(\mathbb{R}^4\) has 4 vectors.
Review the concept: Diagonalization
A square matrix \(A\) is diagonalizable if it is similar to a diagonal matrix \(D\), that is, if it can be written as an invertible matrix \(P\) times \(D\) times the inverse of \(P\).
\[A=PDP^{-1}\]
More practice problems: diagonalization
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