- #1
baggiano
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Hello
I'm trying to show that the following upper bound on the matrix 2-norm is true:
[itex]\left\|(AB)^+\right\|_2\leq\left\|A^+\right\|_2 \left\|B^+\right\|_2[/itex]
where + is the matrix pseudoinverse and [itex]A\in\Re^{n\times m}[/itex] and [itex]B\in\Re^{m\times p}[/itex] are full-rank matrices with [itex]n\geq m\geq p[/itex].
Any hint how I can show it?
Thanks in advance!
Bag
I'm trying to show that the following upper bound on the matrix 2-norm is true:
[itex]\left\|(AB)^+\right\|_2\leq\left\|A^+\right\|_2 \left\|B^+\right\|_2[/itex]
where + is the matrix pseudoinverse and [itex]A\in\Re^{n\times m}[/itex] and [itex]B\in\Re^{m\times p}[/itex] are full-rank matrices with [itex]n\geq m\geq p[/itex].
Any hint how I can show it?
Thanks in advance!
Bag
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