What is the general term of -LRB- x-a -RRB- -LRB- x-b -RRB- -LRB- x-c -RRB- ... -LRB- x-n -RRB- where n is a positive no and a , b , c , ... n are in AP ?
I have a function -LSB- math -RSB- f : \ mathbf -LCB- R -RCB- ^ n \ to \ mathbf -LCB- R -RCB- ^ -LCB- m -RCB- -LSB- / math -RSB- for m > n . How can I define a function -LSB- math -RSB- B : \ mathbf -LCB- R -RCB- ^ n \ to \ mathbf -LCB- R -RCB- ^ -LCB- n \ times m -RCB- -LSB- / math -RSB- such that -LSB- math -RSB- \ forall _ -LCB- X \ in \ mathbf -LCB- R -RCB- ^ n -RCB- -LSB- / math -RSB- the columns of B -LRB- X -RRB- form a basis for the n-hyperplane whose normal vector is parallel to f -LRB- X -RRB- ?