Please answer the following question. Your help is greatly appreciated. For the

Question

Please answer the following question. Your help is greatly appreciated.

For the following functions K(r, z) state if it is a kernel or not. If the function is a kernel, then write down its feature map. If it is not a kernel, prove that it is not one. 1. 21, 22 z1, z2, z1, 22 are real numbers. K(z, z) T122 2. Let ac 1" a 2 21 2d aris and zis are real numbers. K(z, z) 1- (r, z) umbers. K(z, z) 3. aris and zis are real n 21 4. T E ...,zd], z F 21 ...,zd], and f is a function. K(a, z) f(r 1, a2)f(21, 22 3:1, 5. z (T1,...,zd], [21, ...,zd, zis and zis are real numbers. K z,z) zd], aris and zis are integers between 0 and 100. K (z, z) 6. r 3rd, 2 21 min (zi, 2i 7. T F T1, atd., 2 F 21 zd zis and zis are real umbers 8. z zi,..., 3rd, 2 21 zd, ris and zis are integers between 0 and 1 00. K (z, z) 1 max Ei, zi).

Explanation / Answer

Kernel means an empty set

1)Yes because a state cant be a real number

If the imaginary number i is included then there is no meaning to a state

2)Yes

the same reasoning as 1

3) No because distance may be a real number

4)No because they are seperate functions of real and imaginary numbers

5)Yes because the denomination may be irrational

6) Yes

because we cannot compare 3 and (1+i)

7)Yes it a kernel same reasoning as 1

8) Yes same reason as 1 & 2

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