A scalar, which is a tensor of rank 0, is just a number, e.g. 6
A vector, which is a tensor of rank 1, is a group of scalars, e.g. [1, 6, 3]
A matrix, which is a tensor of rank 2, is a group of vectors, e.g.
1 6 3
9 4 2
0 1 3
A tensor of rank 3 would be a group of matrix and would look like a 3d matrix.
A tensor is the general term for all of these, and the generalization into high dimensions.
actually MATRICES is the plural of matrix which means the array of numbers in groups and columns in a rectangular table... and determinant is used to calculate the magnitude of a matrix....
The matrices must have the same dimensions.
Only square matrices have a determinant
In mathematics matrices are made up of arrays of elements.
There are no matrices in the question!
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors.
Tensors are simply arrays of numbers, or functions, that transform according to certain rules under a change of coordinates. Scalars and vectors are tensors of order 0 and 1 respectively. So a vector is a type of tensor. An example of a tensor of order 2 is an inertia matrix. And just for fun, the Riemann curvature tensor is a tensor of order 4.
Only square matrices have inverses.
actually MATRICES is the plural of matrix which means the array of numbers in groups and columns in a rectangular table... and determinant is used to calculate the magnitude of a matrix....
Generally there are two types of physical quantities. One without direction known as scalars other with direction known as vectors. While there are other physical quantities as well that cannot be classified under the two above mentioned categories, they are tensors, matrices, spinors and quaternions.
how is matrices is applicable in our life?
The singular form of matrices is matrix.
Only square matrices have a determinant
The matrices must have the same dimensions.
William John Gibbs has written: 'Tensors in electrical machine theory' -- subject(s): Electrodynamics, Calculus of tensors, Electric machinery
I do not. I f*cking hate matrices. I multiply sheep.
There are no matrices in the question!