What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix? I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A is a matrix). I have been taught that null space is a set of vectors that are squished to 0 when transformation matrix A is applied. Then I came across SVM where kernel functions are used. I read that null spaces are also called kernels of a matrix. My questions are as follows.


Are both kernel functions and null spaces same? If they are related, how are they related?
What is the relation between kernel functions used in SVM and null
    space of matrix? If yes, how? Is this derived from the null space of
    transformations used in SVM?
What is the reasoning behind kernels used in kernel convolution? For
        example: Is the Gaussian kernel used a representation of the
        transformation? How are they related to null spaces? If they are related, how are they related?


Could you please answer these questions? I am very confused. Thank you in advance.
A kernel in the context of digital signal processing refers to the impulse response $h[n]$ of a filter. Particularly for finite length FIR kernels, filtering is carried out by the convolution operator; hence the kernel of the filter is the kernel of the convolution sum. This kernel maps an input vector $x[n]$ into an output vector $y[n]$ i.e., 
$$ y[n] = h[n] \star x[n] = \sum_{k=-\infty}^{\infty} h[k]x[n-k] ~,$$the sum truncated to a finite length for practical FIR convolutions.

As you have described, a null space of a linear mapping is the set of vectors $x$ whose image is the null vector in the range space of the mapping given by the matrix A. As the name implies it is a set of vectors and not a kernel function (sequence). The only kernel in this context is the matrix A which maps input vectors to output vectors, just as in the context of a convolution operator. $$y = A x$$