In “Computing a Neural Network’s Output”

I do not understand how W is a (4,3) matrix, it looks to me it is (4,1) representing w1,w2,w3,w4. Please help me understand.

is it like this ?

w1 | w1 | w1 |

w2 | w2 | w2 |

w3 | w3 | w3 |

w4 | w4 | w4 |

In “Computing a Neural Network’s Output”

I do not understand how W is a (4,3) matrix, it looks to me it is (4,1) representing w1,w2,w3,w4. Please help me understand.

is it like this ?

w1 | w1 | w1 |

w2 | w2 | w2 |

w3 | w3 | w3 |

w4 | w4 | w4 |

**W**is the weight matrix of the**layer 1**(thus the square bracket [1]) that is applied to the input vector**x**=[x1,x2,x3] to output the vector**z**=[z1,z2,z3,z4], which in turn is the input of the activation function sigma to compute the activations**a**=[a1,a2,a3,a4].- Each entry of
**z**is a weighted sum of x1,x2,x3. For example z1[1]=**w**1[1]T.x = w11[1].x1 + w12[1].x2 + w13[1].x3. Thus**w**1[1] has 3 entries (w11[1], w12[1], w13[1]), and to compute all the 4 entries of**z**, you’ll need 4*3=12 parameters. - If you represent
**x**and**z**as matrices, since**z**=wT.**x**and**z**is of dimension (4,1),**x**is of dimension (3,1), w should be of dimension (4,3).

**W**=

**w**1[1]T

**w**2[1]T

**w**3[1]T

**w**4[1]T

=

w11[1] w12[1] w13[1]

w21[1] w22[1] w23[1]

w31[1] w32[1] w33[1]

w41[1] w42[1] w43[1]

Hope this helps!

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