We can express the output of these nodes as vectors. Suppose there are another three layers of nodes. Each of the three nodes in the first layer has a weight associated with its input to the next three nodes. Suppose we have updated the network several times and got the weight semi-random selection in this case. Here, the weights of a row go to the same node in the next layer, and the weights of a column come from the same node in the first layer.
For example, the weight of input node 1 to output node 3 is 0. By multiplying the weight matrix by the input vector, we can calculate the total value of the feed-in node at the next level.
But suppose I want to intervene with each neuron and use a custom activation function. A simple way is to resize each ReLU function from the first level. This will change the graphics of these functions as shown in the following figure:. Now, if these new values are input through the original weight network, we get completely different output values, as shown in the figure:.
If the neural network had worked properly before, we would have destroyed it now. We have to train again to regain the right weight. The value of the first node is twice that of the previous one. Matrix : It is a tabular format in which numbers can be represented, like below — a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 Here, a 11 means 1st row and 1st column.
Rows are horizontal lines and columns are vertical lines. Here, the matrix is 4 x 4. These are shown as n x m, where n is the number of rows and m is the number of columns. Also called the 2-D arrays i. Basic mathematical operations can be done on matrices like Addition, Subtraction, Multiplication, but with some conditions.
Example —. A matrix can be rectangular nXm or square nXn. Tensor : Tensor is like a function, i. It describes an object that is in space. Tensors are of different types — 0 Rank tensors — Scalars 1st Rank tensors — 1-D arrays 2nd Rank tensors — 2-D arrays A matrix nth Rank tensors — n-D arrays So tensor is an n-dimensional array satisfying a particular transformation law. Unlike a matrix, it shows an object placed in a specific coordinate system.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. What are the Differences Between a Matrix and a Tensor?
Ask Question. Asked 8 years, 5 months ago. Active 6 months ago. Viewed k times. Aurelius Aurelius 2, 3 3 gold badges 12 12 silver badges 13 13 bronze badges. You can think of a tensor as a higher-dimensional way to organize information. So a matrix 5x5 for example is a tensor of rank 2. And a tensor of rank 3 would be a "3D-matrix" like a 5x5x5 matrix. I disagree that a tensor of rank 3 would be a "3D matrix", but admittedly it's not uncommon to hear the word "tensor" used in this way.
If you are still confused watch the video from beginning: youtu. Indeed, that video doesn't even explicitly mention matrices at all. Show 3 more comments. Active Oldest Votes. The bottom line of this is: The components of a rank-2 tensor can be written in a matrix. The tensor is not that matrix, because different types of tensors can correspond to the same matrix. The differences between those tensor types are uncovered by the basis transformations hence the physicist's definition: "A tensor is what transforms like a tensor".
In fact, a matrix is not even a matrix, much less a tensor. Could you elaborate or point towards another source to explain this unless I've taken it out of context? The same array of numbers can represent several different basis-independent objects when a particular basis is chosen for them.
Add a comment. Gold Gold That is why it is calles universal property. But, as noted in my answer, in various mathematical contexts there is complication, due, in effect, to "collapsing" in the indexing scheme. But not all matrices represent information that is suitable for such geometric considerations. Muphrid Muphrid Where does it find its justification? Could one construct something similar or analogous for "cobivectors", outer products of 2 covectors, or 2-forms? This could help provide interesting visualizations of 2-forms.
What I'm calling "type" is more rigorously defined but the above gets the gist I think. Tensor must follow the conversion transformation rules, but matrices generally are not. Community Bot 1. Alexander Mathiasen Alexander Mathiasen 21 1 1 bronze badge. Upcoming Events. Featured on Meta. Now live: A fully responsive profile.
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