ëÅ‚ öÅ‚
a11 a12 . . . a1n
ìÅ‚
a21 a22 . . . a2n ÷Å‚
ìÅ‚ ÷Å‚
A =
íÅ‚ Å‚Å‚
. . . . . . . . . . . .
am1 am2 . . . amn
r r
r
rz(A)
A m n
rz(A) d" min{m, n}.
ëÅ‚ öÅ‚
1 2 3 4 5
ìÅ‚ ÷Å‚
0 1 2 -1 3
ìÅ‚ ÷Å‚
A = .
íÅ‚ Å‚Å‚
1 3 5 3 8
2 5 8 7 13
ëÅ‚ öÅ‚ ëÅ‚ öÅ‚
1 2 3 4 5 1 2 3 4 5
ìÅ‚ ÷Å‚ ìÅ‚ ÷Å‚
0 1 2 -1 3 0 1 2 -1 3
ìÅ‚ ÷Å‚ ìÅ‚ ÷Å‚
= .
íÅ‚ Å‚Å‚ íÅ‚ Å‚Å‚
1 - 1 3 - 2 5 - 3 3 - 4 8 - 5 0 1 2 -1 3
2 5 8 7 13 2 5 8 7 13
ëÅ‚ öÅ‚ ëÅ‚ öÅ‚
1 2 3 4 5 1 2 3 4 5
ìÅ‚ ÷Å‚ ìÅ‚ ÷Å‚
0 1 2 -1 3 0 1 2 -1 3
ìÅ‚ ÷Å‚ ìÅ‚ ÷Å‚
= .
íÅ‚ Å‚Å‚ íÅ‚ Å‚Å‚
0 1 2 -1 3 0 1 2 -1 3
2 - 2 · 1 5 - 2 · 2 8 - 2 · 3 7 - 2 · 4 13 - 2 · 5 0 1 2 -1 3
1 2 3 4 5
rz(A) = rz .
0 1 2 -1 3
(-2)
1 2 + (-2) · 1 3 4 5 1 0 3 4 5
rz(A) = rz = rz .
0 1 + (-2) · 0 2 -1 3 0 1 2 -1 3
1 0 3 + (-3) · 1 4 5 1 0 0 4 5
rz(A) = rz = rz .
0 1 2 + (-3) · 0 -1 3 0 1 2 -1 3
(-4)
1 0 0 4 + (-4) · 1 5 1 0 0 0 5
rz(A) = rz = rz .
0 1 2 -1 + (-4) · 0 3 0 1 2 -1 3
(-5)
1 0 0 0 5 + (-5) · 1 1 0 0 0 0
rz(A) = rz = rz .
0 1 2 -1 3 + (-5) · 0 0 1 2 -1 3
1 0
rz(A) = rz .
0 1
1 0
= 1 - 0 = 1,
0 1
rz(A) = 2
ëÅ‚ öÅ‚
2 -1 3 0
íÅ‚ Å‚Å‚
A = 4 -2 6 0 .
5 0 1 2
2 -1 3 0
rzA = rz .
5 0 1 2
0, 5
2 -1 3 0 · 0, 5 2 -1 3 0
rzA = rz = rz .
5 0 1 2 · 0, 5 5 0 1 1
 (-5)
2 + (-5) · 0 -1 3 0 2 -1 3 0
rzA = rz = rz .
5 + (-5) · 1 0 1 1 0 0 1 1
2 -1 3 - 0 0 2 -1 3 0
rzA = rz = rz .
0 0 1 - 1 1 0 0 0 1
2 0
rzA = rz .
0 1
2 0
= 2,
0 1
rzA = 2