How to prove that $DeclareMathOperator{rank}{rank}rank(A) + rank(B) - s leq rank(AB)$
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$A[n times s], B[s times m]$ - matrices
How to prove that
$$rank(A) + rank(B) - s leq rank(AB)$$
I know that
$$rank(AB) leq min(rank(A), rank(B))$$
But it doesn't help me.
Also I know that
$$rank(ABC) = rank(B)$$ if $A$ and $C$ are invertible.
linear-algebra matrix-rank
edited Nov 24 at 10:28
Bernard
117k637110
asked Nov 24 at 8:49
Gorogorov
596
add a comment |
up vote
-2
down vote
favorite
$A[n times s], B[s times m]$ - matrices
How to prove that
$$rank(A) + rank(B) - s leq rank(AB)$$
I know that
$$rank(AB) leq min(rank(A), rank(B))$$
But it doesn't help me.
Also I know that
$$rank(ABC) = rank(B)$$ if $A$ and $C$ are invertible.
linear-algebra matrix-rank
edited Nov 24 at 10:28
Bernard
117k637110
asked Nov 24 at 8:49
Gorogorov
596
Did you search this site? See math.stackexchange.com/q/298836/321264, math.stackexchange.com/q/269474/321264.
– StubbornAtom
Nov 24 at 9:26
Silvester inquelity!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
– Samvel Safaryan
Nov 25 at 10:50
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
$A[n times s], B[s times m]$ - matrices
How to prove that
$$rank(A) + rank(B) - s leq rank(AB)$$
I know that
$$rank(AB) leq min(rank(A), rank(B))$$
But it doesn't help me.
Also I know that
$$rank(ABC) = rank(B)$$ if $A$ and $C$ are invertible.
linear-algebra matrix-rank
edited Nov 24 at 10:28
Bernard
117k637110
asked Nov 24 at 8:49
Gorogorov
596
$A[n times s], B[s times m]$ - matrices
How to prove that
$$rank(A) + rank(B) - s leq rank(AB)$$
I know that
$$rank(AB) leq min(rank(A), rank(B))$$
But it doesn't help me.
Also I know that
$$rank(ABC) = rank(B)$$ if $A$ and $C$ are invertible.
linear-algebra matrix-rank
linear-algebra matrix-rank
edited Nov 24 at 10:28
Bernard
117k637110
asked Nov 24 at 8:49
Gorogorov
596
edited Nov 24 at 10:28
Bernard
117k637110
asked Nov 24 at 8:49
Gorogorov
596
edited Nov 24 at 10:28
Bernard
117k637110
edited Nov 24 at 10:28
Bernard
117k637110
edited Nov 24 at 10:28
Bernard
117k637110
117k637110
asked Nov 24 at 8:49
Gorogorov
596
asked Nov 24 at 8:49
Gorogorov
596
asked Nov 24 at 8:49
Gorogorov
596
596
Did you search this site? See math.stackexchange.com/q/298836/321264, math.stackexchange.com/q/269474/321264.
– StubbornAtom
Nov 24 at 9:26
Silvester inquelity!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
– Samvel Safaryan
Nov 25 at 10:50
add a comment |
Did you search this site? See math.stackexchange.com/q/298836/321264, math.stackexchange.com/q/269474/321264.
– StubbornAtom
Nov 24 at 9:26
Silvester inquelity!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
– Samvel Safaryan
Nov 25 at 10:50
Did you search this site? See math.stackexchange.com/q/298836/321264, math.stackexchange.com/q/269474/321264.
– StubbornAtom
Nov 24 at 9:26
Did you search this site? See math.stackexchange.com/q/298836/321264, math.stackexchange.com/q/269474/321264.
– StubbornAtom
Nov 24 at 9:26
Silvester inquelity!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
– Samvel Safaryan
Nov 25 at 10:50
Silvester inquelity!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
– Samvel Safaryan
Nov 25 at 10:50
add a comment |
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Did you search this site? See math.stackexchange.com/q/298836/321264, math.stackexchange.com/q/269474/321264.
– StubbornAtom
Nov 24 at 9:26
Silvester inquelity!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
– Samvel Safaryan
Nov 25 at 10:50