Matlab: Singular and Nonsingular Matrices 奇異矩陣/非奇異矩陣

inverse matrix 逆矩陣/反矩陣

Nonsingular

If determinant ≠ 0 => i.e. the inverse matrix exists.
=> the matrix is invertible/non-singular.

invertible matrix 可逆矩陣
nonsingular matrix 非奇異矩陣/非特異矩陣

nondegenerate matrix 非退化矩陣

AB = BA = I

B = A^-1 = adj(A)/det(A)

where
adj(A) = adjoint matrix 伴隨矩陣 of A
det(A) = determinant 行列式 of A

>> a = [1 1 ; 2 1]

a =

     1     1
     2     1

>> det(a)

ans =

    -1

>> b = inv(a)

b =

    -1     1
     2    -1

>> a*b

ans =

     1     0
     0     1

>> b*a

ans =

     1     0
     0     1

Singular

If determinant = 0 => the matrix is invertible.

non-invertible matrix 不可逆矩陣

singular matrix 奇異矩陣/特異矩陣
degenerate matrix 退化矩陣

>> a = [2 3;1 1.5]

a =

    2.0000    3.0000
    1.0000    1.5000

>> det(a)

ans =

     0

>> b = inv(a)
Warning: Matrix is singular to working precision. 

b =

   Inf   Inf
   Inf   Inf

>>

Example:

References

奇異矩陣 singular matrix (國家教育研究院雙語詞彙、學術名詞暨辭書資訊網)
Invertible matrix (Wikipedia)