Pedro Arantes
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Matrix Determinant

It's a scalar value that is a function of the entries of a square matrix.
#linear-algebra
Zettelkasten, July 01, 2021

• It's a scalar value that is a function of the entries of a square matrix.

• It represents the area of the parallelogram defined by the vector columns of the matrix.

• If the value is $0$, then:

• the column vectors are linearly dependent.
• If the value is not $0$, then:

• the column vectors are linearly independent;
• the matrix is invertible.

Questions

• In one sentence, shows that $\det(M_1M_2) = \det(M_1)\det(M_2)$.

References

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