Last Updated on January 12, 2026 by Maged kamel
Types of matrices-part 2.
Scalar matrix, Symmetric matrix.
The scalar matrix is the first item: the matrix whose diagonal entries are scalars. For the given matrix, the diagonal is =2, while the remaining elements are all zeros. There are three rows and three columns, so the matrix dimension is 3×3.
The second type of matrix is the symmetric matrix. From its name, a matrix is a symmetrical matrix about the diagonal.
For every I,j aji=aij, for an element above the diagonal element, second row, second column element, a22, we have a12=-3, equal to the component to the left of a22, which is a21, with no change of signs. Similarly, a23=a32=+7, where a23 is in the second and third columns, while a32 is the element in the third row and second columns.
So we will find that aij = aji, a21 = a12, and a23 = a32; a21 = -3, the element in the second row, first column.
While a12=-3, which is the first row, with the second column. a23=7=a32, which is this element, the third row with the second column.
What is the unit matrix-identity matrix?
What is the unit matrix? The unit matrix is one of the three types of matrices. It is a matrix in which all diagonal elements are equal to 0. The diagonal equals 1. The unit matrix is also called the identity matrix. The unit matrix is the multiplicative identity for square matrices in the concept of matrices.
As shown in the next slide, we have a 3×3 matrix.
While the other remaining elements are zeros.
What is a skew-symmetric matrix? It is the matrix for which a =-aji. So for a21=-a12, a23=-a32. In brief, elements are symmetric but change in sign.
What is a triangular matrix?
The 4rth item of the types of matrices is the Triangular Matrix or the echelon form. The matrix can be in one of two forms: an upper triangular matrix or a lower triangular matrix. The main difference can be shown as follows.
The given matrix is 3×3. The elements of the diagonal are 1,4,6. The elements above the diagonal are 3,2,1. The elements below the diagonal are all zeros. The other form is the lower matrix.
The lower matrix has zero values above the diagonal, while the elements below the diagonal have values. The expression for the lower matrix can be written as a for i> or j, which means that, in this case, it has a value.
While aij=0 for i<j. For instance, a23 or the second row with the third column, for which i, or the row number, is < j, which is the column number.
When the row number i is greater than or equal to the column number j, the elements a31, a32, and a33 will have values.
The first-row elements are (2 00), the second-row elements are (4 2 0), and the third-row elements are(0 0 6).
The upper matrix has a definition that is the opposite of the lower matrix’s. The elements below the diagonal are all zeros, while those above the diagonal are non-zero.
The first-row elements are (1 3 2), the second-row elements are (0 4 1), and the third-row elements are(5 8 2).
Transpose of a matrix.
In matrix transpose, we interchange the rows and columns. We have a matrix A, where the first row is( 2 5 4), the second row is(7 6 8), and the third row is ( 2 7 6).
The transpose of a matrix is called “A transpose.” It has a first row, the same as the first column of Matrix A. The first row is (2, 7, 2); as we can see, the second row will be (5, 6, 3), the second column of Matrix A. The third row is the same as the third column in Matrix A, for which the values are (4,8,6).
Press on any image, and you will see a slideshow of pictures 1 and 2, which are included above.
You can view or download the PDf file for the first three posts from the following documents.
For a valid external link, math is fun for the matrix part.
The following post, Matrix operation-part-1. The post includes addition and subtraction of two matrices and the scalar product.
This is a link to the matrix calculator.