1. Square Matrix
That is a matrix with many rows = many columns. In a square matrix, there is a main diagonal, namely entries that have row numbers = column numbers. Example:
In the matrix above it has order 3, and is written A3, while the entries located on the main diagonal are: a11, a22, and a33.
10 Types of Matrix
2. Upper Triangular Matrix
It is a square matrix in which all entries below the main diagonal are zero. Example:
3. Lower Triangular Matrix
It is a square matrix in which all entries above the main diagonal are zero. Example:
4. Diagonal Matrix
It is a square matrix in which all entries outside the main diagonal are zero. Example:
5. Unit Matrix
It is a diagonal matrix whose entries on the main diagonal have a value of one, the symbol: In, n indicates the order of the unit matrix. Example:
6. Scalar Matrix
It is a diagonal matrix where all entries on the main diagonal have the same value, as long as they are not zero, or c≠0. Example:
The effect of multiplying any matrix by a scalar matrix is like multiplying the arbitrary matrix by a scalar c.
7. Zero Matrix
namely a matrix whose entries are all zero. With the symbol: O if the order is important, it is written O35 to indicate a zero matrix with order 3x5. Example:
8. Inverse Matrix
A square matrix A is said to have an inverse if there is a matrix B, so that BA=AB=I is satisfied, the symbol: the inverse of matrix B is usually expressed by A-1. For a 2x2 matrix, the search formula has been given, namely:
For other orders, namely 3x3 etc., the method for finding the matrix inverse will be discussed in the next chapter.
9. Symmetrical Square Matrix
A square matrix is called symmetric, if A = AT Example:
From the example above, it can be seen that the entries on the main diagonal are the mirroring axis, while the entries in the i-th row, j-th column will be mirrored so that they are the same as the entries in the i-th column, j-th row.
10. Skew-Symmetric Square Matrix
A square matrix is called Skew-Symmetric, if AT = -A. Example:
Determine a, b, c, so that matrix A becomes a skew-symmetric matrix, if
Answer:
So we get the equations: a = -1, b = 0, c = -2, 1 = -a, 0 = -b, 2 = -c, meaning: a = -1, b = 0, and c = -2.
