Diagonal matrix refers to a matrix in which all elements except the main diagonal are 0, usually written as diag(a 1, a2, ..., one). Diagonal matrix can be regarded as the simplest matrix, and it is worth mentioning that the elements on the diagonal can be 0 or other values.

Quasi-diagonal matrix;

Quasi-diagonal matrix is a kind of matrix under the concept of block matrix, that is, block matrix is diagonal matrix, and A is block matrix under quasi-diagonal matrix:

Matrix A is a block matrix, and when 2 in A is 0, it is a quasi-diagonal matrix, that is, matrix B is 0. Then the quasi-diagonal matrix is:

E 1=E3。 Of course, E 1 and E3 are not diagonal matrices.

The quasi-diagonal matrix is shown in the following figure:

Diagonal matrix:

Diagonal matrix is a square matrix in which the main diagonal is generally not all zero, and the elements in other positions are all zero.

Extended data

Calculation of diagonal matrix;

Sum and difference operation: the sum and difference of diagonal matrices of the same order are still diagonal matrices.

2. Number multiplication operation: the product of number and diagonal matrix is still diagonal matrix.

3. Product operation: The product of diagonal matrices of the same order is still diagonal matrices, and their products are commutative.

References:

Baidu Encyclopedia-Diagonal Matrix

References:

Baidu Encyclopedia-Block Matrix