Matrix
Perform matrix operations: add, multiply, transpose, determinant
How to use Matrix
- 1Enter the dimensions and values of one or two arrays.
- 2Select the operation: add, multiply, convert, type or reverse matrix.
- 3Views the results matrix or cursor, and shows it in order.
Matrix Operations Base
Multiplier: C ij = Σ A ik x B kj; 2x2 = ad - bcThe matrix is a digital grid; the multiplier is not a factor-by-element multiplication, but a point-cum-column of rows, so the dimensions must be aligned.
Only the square array has a one-sided and reverse matrix; a zero-lined matrix means that it is irreversible.
The most counterintuitive aspect of the matrix multiplication is that it** does not meet the exchange law**, i.e. A x B ≠ B x A (mostly). Because the multiplication code is "A's line and B's column is built in " , it's completely different from the one involved in matching. This means that the "left times" and "right times" of the equation are different and have to be distinguished. The matrix multiplication meets (AB)C = A (BC), which allows complex transformations to be calculated in step.
The geometry of the row is **the linear transformation of the Zoom Multiplier of the area.** Yes, 2x2 matrix, |ad - bc| is the area of the parallel quadrilateral after the transformation of the unit square. Line 0 means that the transformation compresses the plane into a line or a dot (loss of information), at which point the matrix is irreversible — that is, why the reverse request is not one. This geometric perspective is easier to understand than a dead-end formula: "Why is it so big?"
| Operations | Formula (A = [[a,b], [c,d]]) | Type of result | Preconditions |
|---|---|---|---|
| Add | Corresponding Elements Add | Matrix | Two Matrixs Same |
| Multiplication | Each element times k | Matrix | None |
| Multiplication | Line x column for in-house | Matrix | Number of columns of A = rows of B |
| Row | ad − bc | Sample | Square only |
| Inverse Matrix | 1/(ad−bc) × [[d,−b],[−c,a]] | Matrix | Row 0 |
Common Operations for 2x2 Matrix
Frequently asked questions
Why is the matrix size important?
Multiplication requires the number of columns A equal to the number of rows B, otherwise there is no definition.
When does the counter-argument not exist?
, the matrix is strange, unretroverted.
What's the line for?
It shows reversibility and gives a linear change in the area/volume ratio.
What is the use of the matrix?
Very wide. In computer graphics, all matrix operations are smoothing, rotation and scaling (many million array times a second in a 3D game); in machine learning, each layer of the nervous network is a matrix multiplication plus a function; the PageRank algorithm of the search engine is a characterization vector for the matrix; and in economics, input output analysis, circuit analysis, quantum mechanics are based on the matrix. It is one of the most basic mathematical tools of modern technology.
Why is the matrix multiplication so weird?
Because the matrix is a linear shift, and multiplication is a "mixed transformation". When you first change B and then change A, the elements of line I of line I of line AxB, which exactly requires A, line I and row J of line B, are built in. This is the natural result of a complex operation, not an artificial one. When this is understood, the "crowding column" is no longer the rule of the dead, but an inherent logical necessity.