Лекции по векторному и тензорному анализу. Лосик М.В. - 60 стр.

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СГУ им. Чернышевского | Саратов

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P = (P
i
1
...i
p
j
1
...j
q
) (p, q) Q = (Q
i
1
...i
r
j
1
...j
s
)
(r, s) P ·Q
(P · Q)
i
1
...i
p+r
j
1
...j
q+s
= P
i
1
...i
p
j
1
...j
q
Q
i
p+1
...i
p+r
j
q+1
...j
q+s
,
(P ·Q)
i
1
...i
p
r
j
1
...j
q+s
P ·Q
(e
i
) P ·Q (p + r, q + s)
P Q
(P · Q)
i
0
1
...i
0
p+r
j
0
1
...j
0
q+s
= P
i
0
1
...i
0
p
j
0
1
...j
0
q
Q
i
0
p+1
...i
0
p+r
j
0
q+1
...j
0
q+s
=
A
i
0
1
i
1
···A
i
0
p
i
p
A
j
1
j
0
1
···A
j
q
j
0
q
P
i
1
...i
p
j
1
...j
q
A
i
0
p+1
i
p+1
···A
i
0
p+r
i
p+r
A
j
q+1
j
0
q+1
···A
j
q+s
j
0
q+s
Q
i
p+1
...i
p+r
j
q+1
...j
q+s
=
A
i
0
1
i
1
···A
i
0
p+r
i
p+r
A
j
1
j
0
1
···A
j
q+s
j
0
q+s
P
i
1
...i
p
j
1
...j
q
Q
i
p+1
...i
p+r
j
q+1
...j
q+s
=
A
i
0
1
i
1
···A
i
0
p+r
i
p+r
A
j
1
j
0
1
···A
j
q+s
j
0
q+s
(P · Q)
i
1
...i
p+r
j
1
...j
q+s
.
p
P = (P
i
1
...i
p
j
1
...j
q
) (p, q) p, q > 0
r, s 1 ≤ r ≤ p 1 ≤ s ≤ q S
r
s
P
P
(S
r
s
P )
i
1
...i
p−1
j
1
...j
q−1
= P
i
1
...i
r−1
ki
r
...i
p−1
j
1
...j
s−1
kj
s
...j
q−1
(S
r
s
P )
i
1
...i
p−1
j
1
...j
q−1
S
r
s
P
(e
i
) S
r
s
P (p − 1, q − 1)
s = p
r = q P
(S
p
q
P )
i
0
1
...i
0
p−1
j
0
1
...j
0
q−1
= P
i
0
1
...i
0
p−1
k
0
j
0
1
...j
0
q−1
k
0
= A
i
0
1
i
1
···A
i
0
p−1
i
p−1
A
k
0
k
A
j
1
j
0
1
···A
j
q−1
j
0
q−1
A
l
k
0
P
i
1
...i
p−1
k
j
1
...j
q−1
l
.
A
l
k
0
A
k
0
k
= δ
l
k
l
(S
p
q
P )
i
0
1
...i
0
p−1
j
0
1
...j
0
q−1
= A
i
0
1
i
1
···A
i
0
p−1
i
p−1
A
j
1
j
0
1
···A
j
q−1
j
0
q−1
P
i
1
...i
p−1
k
j
1
...j
q−1
k
=
A
i
0
1
i
1
···A
i
0
p−1
i
p−1
A
j
1
j
0
1
···A
j
q−1
j
0
q−1
(S
p
q
P )
i
1
...i
p−1
j
1
...j
q−1
,

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