how to use SVM to classify if the shape of features for each sample is matrix? Is it simply to reshape the matrix to long vector?
Yes, that would be the approach I would recommend. It is essentially the same procedure that is used when utilizing images in image classification tasks, since each image can be seen as a matrix. 
So what people do is to write the matrix as a long vector, consisting of every column concatenated to one another.
So you can do the same here.
I have 120 samples and the shape of features for each sample is matrix of 15*17. how to use SVM to classify? Is it simply to reshape the matrix to long vector?