Scalar Multiplier
Matrix Dimensions
Input Matrix (A)
Operation
Result Matrix (k × A)
How to Use the Calculator
Get your result in three simple steps.
Set Scalar & Dimensions
Enter the scalar value 'k' and use the steppers to set the desired number of rows and columns for your matrix.
Input Your Matrix
Fill in the values for each element in the input matrix (A). The calculator interface will adapt to the dimensions you set.
View Instant Results
The resulting matrix (k × A) is calculated and displayed in real-time in the results monitor, with the operation clearly shown.
What is Scalar Matrix Multiplication?
A fundamental operation in linear algebra.
Scalar multiplication is the process of multiplying a matrix by a single number, known as a scalar. The operation is straightforward: you simply multiply every single element inside the matrix by the scalar value.
If 'k' is the scalar and 'A' is the matrix, the resulting matrix 'B' will have the same dimensions as A, where each element is defined by:
This operation effectively "scales" every component of the matrix. Our scalar matrix calculator automates this element-wise multiplication for matrices of any size.
A Modern Matrix Terminal
Features designed for speed, flexibility, and clarity.
Dynamic Matrix Sizing
Effortlessly change the dimensions of your matrix using the intuitive row and column steppers. The input grid instantly adapts to your needs.
Real-Time Calculation
No 'calculate' button required. The result matrix updates instantly the moment you change the scalar or any element in the input matrix.
Clear & Themed Interface
The distinct two-pane layout and retro-synthwave theme make it easy to distinguish between your inputs and the calculated output.
Where Scalar Multiplication is Used
Practical applications across various scientific fields.
Computer Graphics
Scaling objects up or down. Multiplying a matrix of vertex coordinates by a scalar > 1 enlarges the object, while a scalar between 0 and 1 shrinks it.
Economics & Finance
Adjusting entire portfolios or economic models. For example, applying a growth rate (scalar) to a matrix representing production outputs or asset values.
Data Science
Normalizing data sets. Multiplying a data matrix by a scalar is a key step in feature scaling, which is crucial for many machine learning algorithms to perform well.
