DEV Community: Rohan Yadav The latest articles on DEV Community by Rohan Yadav (@rajrohanyadav). https://dev.to/rajrohanyadav https://media2.dev.to/dynamic/image/width=90,height=90,fit=cover,gravity=auto,format=auto/https:%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Fuser%2Fprofile_image%2F447265%2F6ae47d55-9270-4523-8647-8c4d55ff8101.jpeg DEV Community: Rohan Yadav https://dev.to/rajrohanyadav en What is a Tensor? Rohan Yadav Tue, 08 Sep 2020 15:59:19 +0000 https://dev.to/rajrohanyadav/what-is-a-tensor-3gdm https://dev.to/rajrohanyadav/what-is-a-tensor-3gdm <p>Tensor is one of the most basic concepts to master in Machine &amp; Deep Learning.</p> <h3> Definition </h3> <ul> <li>An n<sup>th</sup> rank tensor in m-dimensional space is a mathematical object that has n indices and m<sup>n</sup> components and obeys certain transformation rules.<sup>1</sup> </li> </ul> <p>Tensors are invariant under a change of coordinates, and have components that change in a special, predictable way if there is a change in coordinates. The tensors in three-dimensional Euclidean space are called Cartesian tensors.</p> <p>Tensors are identified by 3 parameters -</p> <ul> <li> <em>Rank</em>: It represents the number of dimensions of the tensor.</li> <li> <em>Shape</em>: Number of components in each of the dimensions represent shape of the tensor. For Example, for a 2 dimensional tensor, if it has 2 components in first index, and 3 components in the second index, then its shape would be (2,3).</li> <li> <em>Type</em>: It represents the type of data that the tensor contains.</li> </ul> <h3> Popular Terminology </h3> <ul> <li> <strong>Scalars</strong> Tensors with rank = 0, are known as scalars or Rank-0 tensors.</li> <li> <strong>Vectors</strong> Tensors with rank = 1, are known as scalars or Rank-1 tensors.</li> <li> <strong>Matrices</strong> Tensors with rank = 2, are known as scalars or Rank-2 tensors.</li> <li> <strong>Three-Dimensional Arrays</strong> Tensors with rank = 3, are known as scalars or Rank-3 tensors.</li> </ul> <h3> Examples </h3> <div class="ltag_gist-liquid-tag"> </div> <h3> Footnotes </h3> <ul> <li> <sup>1</sup><a href="https://mathworld.wolfram.com/Tensor.html" rel="noopener noreferrer">MathWorld Tensor Definition</a> </li> </ul> tutorial machinelearning beginners deeplearning