값을 입력하면 결과가 즉시 업데이트됩니다. 2×2~6×6 지원.
A determinant is a special scalar value calculated from a square matrix. It tells you if the matrix is invertible, how it scales areas/volumes, and encodes orientation. A zero determinant means the matrix is singular (non-invertible).
라이프니츠 공식: det(A) = Σσ sgn(σ) Πi ai,σ(i). 실제 계산에서는 효율을 위해 소거/분해를 사용합니다.
2×2: det([[a,b],[c,d]]) = ad − bc.
3×3:
4×4: 여인수 전개 또는 LU를 사용하세요. 이 계산기는 내부적으로 LU를 사용합니다.
A complete guide to one of the most important concepts in linear algebra
A determinant is a special scalar value that can be calculated from any square matrix (a matrix with equal rows and columns). Written as det(A) or |A|, it encapsulates fundamental properties of the matrix in a single number.
The determinant tells you whether a system of linear equations has a unique solution, whether a matrix can be inverted, and how transformations affect geometric objects like area and volume.
The absolute value of a 2×2 determinant equals the area of the parallelogram formed by the row vectors.
For 3×3 matrices, the determinant represents the volume of the parallelepiped spanned by the row vectors.
Positive determinant preserves orientation; negative means reflection. Zero means the space is "flattened."
Cramer's Rule uses determinants to solve systems of equations. If det ≠ 0, a unique solution exists.
A matrix has an inverse if and only if its determinant is non-zero. This is fundamental in linear algebra.
Finding eigenvalues requires solving det(A − λI) = 0, essential in physics and engineering.
Transformations in 3D graphics use matrices. The determinant reveals if shapes are flipped or scaled.
Watch how determinants are calculated step-by-step with interactive examples
Calculations update in real-time as you type
Support for 2×2 up to 6×6 matrices
See the calculation process explained
Copy results or matrices with one click
입력을 분석해 실시간으로 행렬식을 계산합니다. 수치 안정성과 성능을 위해 부분 피벗팅 LU 분해를 사용합니다. 결과는 U의 대각 원소의 곱에 행 교환으로 인한 부호를 곱한 값입니다.
