This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.

This 27-minute video lesson shows that any member of Rn can be represented as a unique sum of a vector in subspace V and a vector in the orthogonal complement of V.

This 7-minute video lesson gives an alternative (short cut) for calculating 3x3 determinants (Rule of Sarrus).

This 9-minute video lesson shows how to calculate a 4x4 determinant by putting in in upper triangular form first.

This 19-minute video lesson finds an orthonormal basis for a subspace using the Gram-Schmidt Process.

This 8-minute video lesson looks at the determinant of an upper triangular matrix.

This 9-minute video lesson provides definitions of the vector dot product and vector length.

This video shows that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n

This 19-minute video lesson shows how to define the determinant for nxn matrices. And it provides an exampled of a 4x4 determinant.

Jill Bolte Taylor got a research opportunity few brain scientists would wish for: She had a massive stroke, and watched as her brain functions -- motion, speech, self-awareness -- shut down one by one. An astonishing story.

This is a supplementary video for the Commonwealth of Learning Open Textbook Manual. It shows how to create Lessons in OER Commons. The OER Commons Lesson Builder allows instructors to create resources that are viewable by students as lessons, and by teachers as lesson plans with supplemental instructional resources.

This is a supplementary video to support the Commonwealth of Learning's Open Textbook Manual. It shows you how to use the OER Commons Open Author Tool to create Open Textbooks.

This 15-minute video lesson gives an example involving the preimage of a set under a transformation. It also gives a definition of kernel of a transformation.

Now more than ever, it's important to look boldly at the reality of race and gender bias -- and understand how the two can combine to create even more harm. Kimberlé Crenshaw uses the term "intersectionality" to describe this phenomenon; as she says, if you're standing in the path of multiple forms of exclusion, you're likely to get hit by both. In this moving talk, she calls on us to bear witness to this reality and speak up for victims of prejudice.

When stress got to be too much for TED Fellow Sangu Delle, he had to confront his own deep prejudice: that men shouldn't take care of their mental health. In a personal talk, Delle shares how he learned to handle anxiety in a society that's uncomfortable with emotions. As he says: "Being honest about how we feel doesn't make us weak -- it makes us human."

Is love a signal winding through your neural pathways? A cliche? A cult? Love is easy to compare but difficult to define, maybe because we’re fundamentally biased; we try to define love while falling in or out of it. And love feels differently to every person who feels it, but this subjective emotion has evolutionary explanations, too. Brad Troeger takes a shot at the definition of love.

A brief video where OER experts give their reasons for working in the field of Open Educational Resources. Primary reasons include empowering teachers, equalizing access to education, reducing teachers' worries about copyright, reducing educational costs, and facilitating the open flow of information.

How many times does the chorus repeat in your favorite song? How many times have you listened to that chorus? Repetition in music isn’t just a feature of Western pop songs, either; it’s a global phenomenon. Why? Elizabeth Hellmuth Margulis walks us through the basic principles of the ‘exposure effect,’ detailing how repetition invites us into music as active participants, rather than passive listeners.