## Saturday, 8 June 2013

### MATRICES: SIGNIFICANCE & PURPOSE

|||| MATRICES are a way to help us understand the design or the content of an object in real-life when put on a paper in a block-format.

Examples of matrices in real life.

BUT WHERE TO USE MATRICES?  HOW DO WE KNOW WHEN AND WHEN NOT TO USE MATRICES?

|||| Everything under the sun can be put into a matrix-format. Einstein put the whole universe in a 4-dimensional matrix: 3 dimensions of space & one dimension of time.

|||| Well, its just a question of whether it would be useful for you to do so.

|||| Basically, the graph paper that you use is also a matrix.

|||| The latitudes and longitudes are also a matrix.

THE TRANSPOSE OF A MATRIX.

|||| The transpose of a matrix basically is nothing but the whole matrix ( or the object which you are representing as a matrix) rotates by 180 degrees.

|||| The diagonal of the matrix is the axis along which the object is rotated.

|||| Now obviously , if you rotate the object twice by 180 degree, the object  comes back to how it was.

|||Transpose of A = Rotation by 180 degrees.

|||| Therefore Transpose of (Transpose of A)= Rotation by 360 degrees = A

|||| Thus transpose of ( transpose of A) = A is like saying that if you take a matrix A, rotate it first by 180 degree and then once more by 180 degree, A will come back to as it is .

THE DIAGONAL OF A MATRIX.

|||| The diagonal of a matrix is very similar to the axle of car.

|||| You may have wondered why the diagonal elements of a matrix remain where they in spite of operations like taking a transpose.

APPLICATION OF MATRICES.

|||| Imagine a map. On this map you are plotting the height of every form of landscape of India.

|||| Where there are mountains, In your matrix, obviously, the content in that block of the matrix will go high.

|||| On sea, level, the value of that block in the matrix will be zero.

|||| If the value in the matrix at any point goes below zero, that place is below sea-level (i.e a mine or something).