Linear algebra matrix and tensor operations vectors and tensors

vec = {1, 2, 3}

{1, 2, 3}

Range[10]

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Range[1., 4, 0.1]

{1., 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7000000000000002, 1.8, 1.9, 2., 2.1, 2.2, 2.3, 2.4000000000000004, 2.5, 2.6, 2.7, 2.8, 2.9000000000000004, 3., 3.1, 3.2, 3.3000000000000003, 3.4000000000000004, 3.5, 3.6, 3.7, 3.8000000000000003, 3.9000000000000004, 4.}

vec = Table[Sqrt[i / 2.], {i, 5}]

{0.7071067811865476, 1., 1.224744871391589, 1.4142135623730951, 1.5811388300841898}

vec = Sqrt[Range[5] / 2.]

{0.7071067811865476, 1., 1.224744871391589, 1.4142135623730951, 1.5811388300841898}

vec  + 4

{4.707106781186548, 5., 5.224744871391589, 5.414213562373095, 5.58113883008419}

vec[[2]]

1.

vec[[4]] = x;
vec

{0.7071067811865476, 1., 1.224744871391589, x, 1.5811388300841898}

tensor = Table[1 / (i j k), {i, 2}, {j, 3}, {k, 4}]

{{{1, 1/2, 1/3, 1/4}, {1/2, 1/4, 1/6, 1/8}, {1/3, 1/6, 1/9, 1/12}}, {{1/2, 1/4, 1/6, 1/8}, {1/4, 1/8, 1/12, 1/16}, {1/6, 1/12, 1/18, 1/24}}}

tensor[[1, 2, 1]]

1/2

MatrixQ[{{1, 2, 3}, {4, 5, 5}}]

True

VectorQ[{1, 2, 3}]

True

ArrayQ[ {{{1, 2}, {3, 4}}, {{4, 5}, {6, 7}}}]

True

ArrayQ[ {{{1, 2}, {3, 4}}, {{4, 5}, {6, 7}}}, 3]

True

ArrayQ[ {{{x, 2}, {3, 4}}, {{4, 5}, {6, 7}}}, 3, NumberQ]

False

Dimensions[{{{1, 2}, {3, 4}}, {{4, 5}, {6, 7}}}]

{2, 2, 2}

ArrayDepth[ {{1, 2, 3}, {4, 5, 6}}]

2

ten = {{{1, 2}, {3, 4}}, {{4, 5}, {6, 7}}};
ten == ten

True

ten == N[ten]

True

ten == {1, 2, 3}

False