How to bring the matrix to canonical form

Remember that the canonical form of the matrix does not require that in all main diagonal standing units. The essence of the definition lies in the fact that the only nonzero elements of the matrix in its canonical form is a unit. If they are present, are located on the main diagonal. However, their number can vary from zero to the number of lines in the matrix.

Don't forget that elementary transformations allow any matrix lead to the canonical mind. The biggest difficulty – intuitive to find the simplest sequence of chains of actions and not to make a mistake in calculations.

Learn the basic properties of the operations with rows and columns in the matrix. To the elementary transformations include three standard conversions. This multiplication of lines of the matrix by any nonzero number, sum lines (including the addition to one another, multiplied by some number) and permutation. Such actions allow to obtain a matrix equivalent to this. Respectively you can perform such operations with columns and without loss of equivalence.

Try not to simultaneously perform several elementary transformations: move from stage to stage in order to prevent random error.

Find the rank of a matrix, to determine the number of units on the main diagonal: this will tell you what the final look will have the desired canonical form, and will eliminate the need to perform conversions, if you just want to use it for.

Use the method of the fringe of the minors in order to perform the previous recommendation. Calculate the minor of the K-th order, and also bordering all its minors of degree (K+1). If they are equal to zero, then the rank of a matrix is the number of K. do Not forget that minor M is the determinant of the matrix obtained by striking out row i and column j from the original.