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Rank of a Matrix

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Instructor: Niraj Singh

Language: English/Hindi

In linear algebra, the rank of a matrix A is the dimension of the vector space generated by its columns. This corresponds to the maximal number of linearly independent columns of A. This, in turn, is identical to the dimension of the vector space spanned by its rows. 
A matrix's rank is one of its most fundamental characteristics. The rank is commonly denoted by rank(A) or rk(A)

We have further divided this chapter into the following classes:

  • Class A:  In this class, we will solve problems related to theorems based on hermitian, skew-hermitian, symmetric, skew-symmetric matrices

  • Class B: In this class, we will solve problems related to properties of orthogonal and unitary matrices

  • Class C: In this class, we will solve problems based on finding the rank of matrices through normal form reduction.

  • Class D: In this class, we will solve problems based on a reduction to PAQ normal form.
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