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I have a column vector and am trying to convert it into a new coordinate system. The way I would like to do this is to start with a column vector of size 1x300, corresponding to 100 1x3 vectors all in one column. I then have 3 matrices A, B and C which are all of size 3x100 each corresponding to 100 vectors in an array. I need to take the first vector from the column and multiply the transpose with the the first vector from the array A to get a scalar which is the first entry in a new column vector, then multiply it with the first vector from B for the second entry and multiply it with the first vector from C for the third entry.

I would then repeat this with all the vectors to get a new 1x300 column vector (this corresponds to converting to a new coordinate system I have created). Let me know if that doesn't make sense or if further explanation is required.

Basically, there are 100 1x3 vectors on top of each other in a column corresponding to 100 nodes, then the the 3 arrays correspond to the normal vectors and two tangent vectors at the 100 nodes, so I am taking each node and multiplying it with the normal at that node (ie. first vector from array A), then the two tangents at that node (ie. first vectors from arrays B and C) to get the vector in the new coordinate system, this is then repeated for all the nodes to get a new column vector.

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