Scalar vs Vector vs Matrix vs Tensor

• Scalar

0-dimensional, a data consisting of a single real value. For example, your speed is a scalar value because it only has one component, how fast you are going. Your height is also a scalar value because the only component is how tall you are. 

 

• Vector

1-dimensional array or list. 1-dimensional tensor.

np.array([1,2,3])
>>>
array([1, 2, 3])

 

• Matrix

2-dimensional which has row and column.

np.array([[1,2,3],[4,5,6]])
>>>
array([[1, 2, 3],
       [4, 5, 6]])

 

• Tensor

Over 3-dimensional

np.array([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]])
>>>
array([[[ 1,  2,  3],
        [ 4,  5,  6]],

       [[ 7,  8,  9],
        [10, 11, 12]]])

 

• Matrix Operation

Hypothesis : Predict one y with multiple x.

 

It can be expressed as vectors.

Or

 

Let's take this.

Hypothesis : Predict one y with multiple x.

 

H(X)=XW+B And added B.

Or

H(X)=WX+B

For instance, (batch_dim, input_dim) * (input_dim, output_dim) + b = (batch_dim, output_dim)

dimension : output_dim = b

For instance,

(1, 4) * (4, 2) + 2 = (1, 2)

(5, 4) * (4, 3) + (5, 3) = (5, 3)

• sample

Divided data into coutable units.

 

• feature

Each x(independent variable).