I know in order to shrink or expand the number of channels a 1x1 convolution is performed. I need to clarify the following: is the 1x1 convolution(s) just a matrix multiplication between the image with shape (h w, 3) (RGB) and a matrix that holds the learnable weights with shape (3, 1)? Which will result in a new matrix of shape (h w, 1) (in this case the number of channels shrunk from 3 to 1). If the above is correct, what happens under the hood of a NN framework, such as PyTorch, when the number of input channels is equal to the number of output channels? Does a matrix multiplication take place between the input (h*w, 3) and a matrix with learnable weights (num_channels, num_channels)? Doesn't this introduce unnecessary (and unwanted) operations?

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