Linear Algebra Calculators

Learn Linear Algebra the Friendly Way

Welcome! If you've ever worked with matrices or vectors and wished for a bit more clarity, you're in the right place. Linear algebra is everywhere—from computer graphics to Physics—and understanding it doesn’t have to be tricky. With the help of our online calculators, you can check your answers, test your understanding, or just save time on long computations.

From finding determinants to breaking down matrices into parts, we've got tools that handle the heavy lifting. Let’s walk through how these tools can make learning and using linear algebra feel much more manageable.

Break Down Big Ideas With Easy Tools

Linear algebra can feel like a maze. There's a lot going on—systems of equations, transformations, and matrix operations. But using the right tool helps untangle the confusion.

• The LU Decomposition Calculator lets you break a matrix into lower and upper triangular parts. It’s great for solving systems step by step.
• The QR Factorization Calculator and QR Decomposition Calculator provide another way to split a matrix—handy for numerical methods and stability.
• If you're trying to diagonalise a matrix, the Diagonalise Matrix Calculator shows you the path to eigenvalues and eigenvectors.
• Want to simplify a system of equations? The Gauss-Jordan Elimination Calculator guides you through it row by row.
• Check if a matrix can be inverted with the Matrix Inverse Calculator, or get a best-fit solution with the Pseudoinverse Calculator.

These tools help you see patterns and processes more clearly without getting bogged down in arithmetic.

Get Answers Fast Without Guessing

Sometimes you just need to check your work or get a quick answer without working out every step by hand.

• Add, subtract, or multiply matrices with the Matrix Addition Calculator, Matrix Subtraction Calculator, or Matrix Multiplication Calculator.
• Scale a matrix or divide one by a scalar using the Matrix Scalar Multiplication Calculator and Matrix Division Calculator.
• If you're handling powers or exponentials, try the Matrix Power Calculator or Matrix Exponential Calculator to manage tough computations.
• Need the transpose or trace? Use the Matrix Transpose Calculator or Matrix Trace Calculator.
• The Matrix of Minors Calculator assists with building cofactors and solving for inverses manually.

These calculators save time and make checking your work a breeze.

Vectors Don’t Have to Be Vague

Vectors are just as central to linear algebra as matrices. And we’ve got tools to help with them too.

• Combine forces or directions with the Vector Addition Calculator and Vector Subtraction Calculator.
• Stretch or shrink a vector using the Vector Scalar Multiplication Calculator.
• Find how long a vector is with the vector magnitude Calculator and turn it into a unit vector with the Unit Vector Calculator.
• Need to know how much of one vector lies along another? Try the Vector Projection Calculator and Scalar Projection Calculator.
• The Cross Product Calculator and Dot Product Calculator help you understand how vectors interact in 2D or 3D space.
• For more complicated problems, the triple scalar product Calculator can assist with volume or orientation in 3D.

These tools help you build intuition by letting you play with values and see what happens.

Explore Spaces and Dimensions with Confidence

Linear algebra isn’t just about crunching numbers—it’s about understanding shapes, directions, and spaces. Our calculators help reveal what’s really going on behind the numbers.

• The Null Space Calculator shows which vectors make a matrix equation equal zero.
• Use the Column Space Calculator to see what outputs a matrix can actually produce.
• Want to know if vectors stand alone or depend on each Other? Use the Linear Independence Calculator.
• The Matrix Rank Calculator tells you how many dimensions a matrix really spans.

These ideas are key in everything from solving systems to analysing transformations—and our tools help make the ideas concrete.

Build Deeper Understanding Through Structure

If you're ready to go beyond the basics, these tools help you see how matrices are built and what they tell you.

• Use the Characteristic Polynomial Calculator to find eigenvalues the classic way.
• Get a deeper look at matrix behaviour with the Eigenvalue and Eigenvector Calculator.
• Break down any matrix using the SVD Calculator for singular value decomposition.
• Want to test how a matrix transforms space? Try the Vector Calculator for flexible operations.

Each calculator opens a small window into how linear algebra describes movement, shape, and direction—and why those things matter in real life.

Try any of these calculators now and make your next linear algebra problem feel much easier.