Quadratic matrix/Rank/Invertible/Linearly independent/Fact

< Quadratic matrix < Rank < Invertible < Linearly independent

Let be a field, and let denote an -matrix over . Then the following statements are equivalent.

  1. is invertible.
  2. The rank of is .
  3. The rows of are linearly independent.
  4. The columns of are linearly independent.
Proof, Write another proof
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