Films · Mathematics · Matrices
Prof. Dr. Dirk Schieborn
Higher Mathematics 1 · Reutlingen University
Lecture film · Higher Mathematics 1
Ones, Antimatter, a Phone Number: Identity Matrix, Inverse and A · x = b
Lecture film · Higher Mathematics 1
Ones, Antimatter, a Phone Number: Identity Matrix, Inverse and A · x = b
Prof. Dr. Dirk Schieborn
Higher Mathematics 1 · Reutlingen University
The neutral element for times is the identity matrix, not the matrix full of ones. Its counterpart is the inverse: A⁻¹ · A = E. It turns the system A · x = b into the solution x = A⁻¹ · b, provided A⁻¹ exists. The phone number matrix has none.
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Ones, Antimatter, a Phone Number: Identity Matrix, Inverse and A · x = b
Prof. Dr. Dirk SchiebornHigher Mathematics 1 · Reutlingen UniversityAn explainer film in six chapters, made from a real lecture: which matrix plays the role of zero and one, why the matrix full of ones is not neutral, the identity matrix, the inverse as its counterpart like matter and antimatter, the system of equations in five symbols A · x = b, the solution x = A⁻¹ · b and Gauss-Jordan elimination on the phone number matrix, which has no inverse. Pause anywhere and ask.
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