Takashi Takiguchi

This book addresses a gap in elementary linear algebra: while solving systems of linear equations with multiple solutions is standard, analyzing overdetermined systems with no solution—common in practical applications—is rarely taught. We develop a theory for such systems using the concept of least-squares solutions, grounded entirely in elementary linear algebra. Unlike approaches based on the Moore–Penrose inverse, which require advanced tools such as singular value decomposition, our method relies only...