Linear TransformationsWhat makes a map linear, and the four subspaces every matrix carries.MathematicsA map that respects addition and scaling.What makes a map linearT(u + v) = T(u) + T(v)T(λv) = λT(v)T(0) = 0 then follows, alwaysFix a basis and every linear map is a matrixThe four subspaces of AColumn space — the image of the mapNull space — vectors sent to zeroRow space — sits in the domainLeft null space — sits in the codomainColumn space and left null space are orthogonal complements in thecodomain; row space and null space are complements in the domain.Linear Transformationslearnposters.com
Linear Transformations — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Linear Transformations poster

8 entries in 2 groups.

A map that respects addition and scaling.

Column space and left null space are orthogonal complements in the codomain; row space and null space are complements in the domain.

Questions about the Linear Transformations poster

What’s on the Linear Transformations poster?
8 entries in 2 groups. A map that respects addition and scaling. What makes a map linear: T(u + v) = T(u) + T(v), T(λv) = λT(v), T(0) = 0 then follows…; The four subspaces of A: Column space — the image of the map, Null space — vectors se…. Column space and left null space are orthogonal complements in the codomain; row space and null space are complements in the domain.
Who is the Linear Transformations poster for?
Linear Transformations belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning linear algebra can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Linear Transformations poster?
When you need to check linearity, or locate the image and kernel of a matrix. A wall chart earns its place by being glanceable from where the work is happening, so Linear Transformations belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Linear Transformations?
Basis & Dimension, Determinant Properties and Diagonalisation sit alongside Linear Transformations in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Basis & DimensionDeterminant PropertiesDiagonalisation
Is the Linear Transformations poster free to download and print?
Yes. Linear Transformations downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Linear Transformations poster print at?
Linear Transformations is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Linear Transformations loses nothing.Printing guide

Related posters

Charts that sit alongside Linear Transformations on the same wall.

Browse every Mathematics poster, or start from the full catalogue.